Abstract group data - 51840.cr

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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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 240, 'aut_gen_orders': [8, 12, 8, 12, 4], 'aut_gens': [[1, 4, 320, 960, 2880, 17280], [1753, 13452, 6720, 42240, 39360, 6080], [3425, 13868, 41920, 11520, 49280, 37120], [17945, 5868, 25600, 48320, 32640, 12160], [433, 30508, 25280, 2240, 22720, 41920], [16577, 21452, 1920, 40640, 14400, 28800]], 'aut_group': None, 'aut_hash': 944450307074591112, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 103680, 'aut_permdeg': 2808, 'aut_perms': 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'aut_phi_ratio': 7.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 1, 2], [2, 90, 1, 2], [3, 80, 1, 1], [4, 162, 1, 2], [4, 810, 1, 2], [4, 1080, 2, 2], [5, 324, 1, 1], [6, 80, 1, 1], [6, 720, 1, 2], [8, 162, 1, 4], [8, 1620, 1, 2], [8, 3240, 2, 2], [10, 324, 1, 3], [12, 2160, 2, 2], [16, 324, 2, 2], [16, 1620, 2, 2], [20, 324, 1, 4], [40, 324, 1, 8], [80, 324, 2, 8]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_3^4.C_{80}:C_2.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 240, 'autcentquo_group': '25920.dn', 'autcentquo_hash': 1549518908401167474, 'autcentquo_nilpotent': False, 'autcentquo_order': 25920, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{81}:C_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 81, 2], [2, 90, 2], [3, 80, 1], [4, 162, 2], [4, 810, 2], [4, 1080, 4], [5, 324, 1], [6, 80, 1], [6, 720, 2], [8, 162, 4], [8, 1620, 2], [8, 3240, 4], [10, 324, 3], [12, 2160, 4], [16, 324, 4], [16, 1620, 4], [20, 324, 4], [40, 324, 8], [80, 324, 16]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '25920.dn', 'commutator_count': 1, 'commutator_label': '3240.b', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '5.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 70, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['25920.dn', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 1, 2], [2, 90, 1, 2], [3, 80, 1, 1], [4, 162, 1, 2], [4, 810, 1, 2], [4, 1080, 2, 2], [5, 324, 1, 1], [6, 80, 1, 1], [6, 720, 1, 2], [8, 162, 2, 2], [8, 1620, 1, 2], [8, 3240, 2, 2], [10, 324, 1, 3], [12, 2160, 2, 2], [16, 324, 2, 2], [16, 1620, 2, 2], [20, 324, 2, 2], [40, 324, 4, 2], [80, 324, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 423198720, 'exponent': 240, 'exponents_of_order': [7, 4, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[80, 0, 2], [80, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '51840.cr', 'hash': 8363559991699411848, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 240, 'inner_gen_orders': [4, 80, 3, 3, 3, 3], 'inner_gens': [[1, 12, 40640, 23040, 22400, 30720], [313, 4, 48000, 12480, 21120, 19520], [28801, 24324, 320, 960, 2880, 17280], [47041, 5764, 320, 960, 2880, 17280], [36161, 36484, 320, 960, 2880, 17280], [6721, 1604, 320, 960, 2880, 17280]], 'inner_hash': 1549518908401167474, 'inner_nilpotent': False, 'inner_order': 25920, 'inner_split': True, 'inner_tex': 'F_{81}:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': 80, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 80, 'irrep_stats': [[1, 16], [2, 12], [4, 36], [80, 8]], 'label': '51840.cr', 'linC_count': 4, 'linC_degree': 80, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 80, 'linQ_degree_count': 2, 'linQ_dim': 80, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 80, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*F81:C4', 'ngens': 12, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 54, 'number_characteristic_subgroups': 50, 'number_conjugacy_classes': 72, 'number_divisions': 38, 'number_normal_subgroups': 68, 'number_subgroup_autclasses': 377, 'number_subgroup_classes': 450, 'number_subgroups': 96258, 'old_label': None, 'order': 51840, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 343], [3, 80], [4, 6264], [5, 324], [6, 1520], [8, 16848], [10, 972], [12, 8640], [16, 7776], [20, 1296], [40, 2592], [80, 5184]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[8641, 8644, 320, 960, 2880, 17280], [1, 8644, 320, 960, 2880, 17280]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 83, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 8], [8, 4], [16, 2], [32, 2], [80, 4], [160, 2]], 'representations': {'PC': {'code': '7819445550637814139274665157217293082331874833444081189430809478627690884888563167712905070282788127619706093222095475888713926999546373091252113933147182207577245521591907097009438843839883023270489537424397677073728214484118014374828147460643605335177419069098822981', 'gens': [1, 3, 8, 9, 10, 12], 'pres': [12, 2, 2, 2, 2, 2, 2, 5, 3, 3, 2, 3, 3, 24, 434, 662, 98, 1155, 1743, 135, 2884, 4336, 172, 6917, 10385, 209, 16134, 10770, 3901447, 92179, 1152031, 19243, 145975, 138307, 44239, 2488328, 34580, 336992, 337004, 38936, 61628, 1160, 2688009, 960021, 633633, 753645, 338457, 19269, 61881, 357, 5533450, 908182, 1393954, 517486, 150538, 30430, 100402, 4423691, 1336343, 702755, 5807, 14459, 167111, 52643]}, 'Perm': {'d': 83, 'gens': [58989429424868087701723073455260162573691759407529021502448720191153849893169722005993899938094400204804193241065837165494, 498842762063482275731453552732125518937867133980465278230709788333357352245418643242627014194609495130447734701374254948206, 1954577286648981654821137590207589065667040243969822746003136707912282259154209247023475012219773868463578345951875355956064, 1461675729899916178393275329927689338386828061845320517481760963151067259591386504950846958585694225467780124368157060867206, 41452341653778513112146351079237148570177191192819237258525756044022350089949007763371313459595892381840954117425727626367, 980439065479413001170172470921200096139537654692067946496914387567160193446415875626933214554056121825678394975040587433894, 46391436795846896736769733099773986709645539479246750464818898103875986194066047907999533831602467952640766608496092108015]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times F_{81}:C_4', 'transitive_degree': 162, '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: 163589923
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 70, 'group_order': 51840, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 163589934
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 70, 'group_order': 51840, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8640, 'size': 1}
  • id: 163589945
    {'aut_label': '2B', 'centralizer': '81.a1.a1', 'counter': 3, 'group_counter': 70, 'group_order': 51840, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 28960, 'size': 81}
  • id: 163589956
    {'aut_label': '2C', 'centralizer': '81.a1.a1', 'counter': 4, 'group_counter': 70, 'group_order': 51840, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 32160, 'size': 81}
  • id: 163589967
    {'aut_label': '2D', 'centralizer': '90.a1.a1', 'counter': 5, 'group_counter': 70, 'group_order': 51840, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 162, 'size': 90}
  • id: 163589978
    {'aut_label': '2E', 'centralizer': '90.a1.a1', 'counter': 6, 'group_counter': 70, 'group_order': 51840, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 32578, 'size': 90}
  • id: 163589989
    {'aut_label': '3A', 'centralizer': '80.f1.a1', 'counter': 7, 'group_counter': 70, 'group_order': 51840, 'label': '3A', 'order': 3, 'powers': [7, 1, 7], 'representative': 5760, 'size': 80}
  • id: 163589993
    {'aut_label': '4A', 'centralizer': '162.c1.a1', 'counter': 8, 'group_counter': 70, 'group_order': 51840, 'label': '4A', 'order': 4, 'powers': [3, 8, 8], 'representative': 5840, 'size': 162}
  • id: 163589994
    {'aut_label': '4B', 'centralizer': '162.c1.a1', 'counter': 9, 'group_counter': 70, 'group_order': 51840, 'label': '4B', 'order': 4, 'powers': [3, 9, 9], 'representative': 26000, 'size': 162}
  • id: 163589924
    {'aut_label': '4C', 'centralizer': '810.b1.a1', 'counter': 10, 'group_counter': 70, 'group_order': 51840, 'label': '4C', 'order': 4, 'powers': [3, 10, 10], 'representative': 14066, 'size': 810}
  • id: 163589925
    {'aut_label': '4D', 'centralizer': '810.b1.a1', 'counter': 11, 'group_counter': 70, 'group_order': 51840, 'label': '4D', 'order': 4, 'powers': [3, 11, 11], 'representative': 22290, 'size': 810}
  • id: 163589926
    {'aut_label': '4E1', 'centralizer': '1080.a1.a1', 'counter': 12, 'group_counter': 70, 'group_order': 51840, 'label': '4E1', 'order': 4, 'powers': [5, 13, 12], 'representative': 281, 'size': 1080}
  • id: 163589927
    {'aut_label': '4E-1', 'centralizer': '1080.a1.a1', 'counter': 13, 'group_counter': 70, 'group_order': 51840, 'label': '4E-1', 'order': 4, 'powers': [5, 12, 13], 'representative': 123, 'size': 1080}
  • id: 163589928
    {'aut_label': '4E1', 'centralizer': '1080.a1.a1', 'counter': 14, 'group_counter': 70, 'group_order': 51840, 'label': '4F1', 'order': 4, 'powers': [5, 15, 14], 'representative': 22377, 'size': 1080}
  • id: 163589929
    {'aut_label': '4E-1', 'centralizer': '1080.a1.a1', 'counter': 15, 'group_counter': 70, 'group_order': 51840, 'label': '4F-1', 'order': 4, 'powers': [5, 14, 15], 'representative': 9291, 'size': 1080}
  • id: 163589930
    {'aut_label': '5A', 'centralizer': '324.d1.a1', 'counter': 16, 'group_counter': 70, 'group_order': 51840, 'label': '5A', 'order': 5, 'powers': [16, 16, 1], 'representative': 47616, 'size': 324}
  • id: 163589931
    {'aut_label': '6A', 'centralizer': '80.f1.a1', 'counter': 17, 'group_counter': 70, 'group_order': 51840, 'label': '6A', 'order': 6, 'powers': [7, 2, 17], 'representative': 2880, 'size': 80}
  • id: 163589932
    {'aut_label': '6B', 'centralizer': '720.e1.a1', 'counter': 18, 'group_counter': 70, 'group_order': 51840, 'label': '6B', 'order': 6, 'powers': [7, 5, 18], 'representative': 1442, 'size': 720}
  • id: 163589933
    {'aut_label': '6C', 'centralizer': '720.e1.a1', 'counter': 19, 'group_counter': 70, 'group_order': 51840, 'label': '6C', 'order': 6, 'powers': [7, 6, 19], 'representative': 39618, 'size': 720}
  • id: 163589935
    {'aut_label': '8A1', 'centralizer': '162.c1.a1', 'counter': 20, 'group_counter': 70, 'group_order': 51840, 'label': '8A1', 'order': 8, 'powers': [8, 20, 21], 'representative': 13800, 'size': 162}
  • id: 163589936
    {'aut_label': '8A-1', 'centralizer': '162.c1.a1', 'counter': 21, 'group_counter': 70, 'group_order': 51840, 'label': '8A-1', 'order': 8, 'powers': [8, 21, 20], 'representative': 25240, 'size': 162}
  • id: 163589937
    {'aut_label': '8B1', 'centralizer': '162.c1.a1', 'counter': 22, 'group_counter': 70, 'group_order': 51840, 'label': '8B1', 'order': 8, 'powers': [8, 22, 23], 'representative': 33080, 'size': 162}
  • id: 163589938
    {'aut_label': '8B-1', 'centralizer': '162.c1.a1', 'counter': 23, 'group_counter': 70, 'group_order': 51840, 'label': '8B-1', 'order': 8, 'powers': [8, 23, 22], 'representative': 32200, 'size': 162}
  • id: 163589939
    {'aut_label': '8C', 'centralizer': '1620.b1.a1', 'counter': 24, 'group_counter': 70, 'group_order': 51840, 'label': '8C', 'order': 8, 'powers': [8, 24, 24], 'representative': 45642, 'size': 1620}
  • id: 163589940
    {'aut_label': '8D', 'centralizer': '1620.b1.a1', 'counter': 25, 'group_counter': 70, 'group_order': 51840, 'label': '8D', 'order': 8, 'powers': [8, 25, 25], 'representative': 23658, 'size': 1620}
  • id: 163589941
    {'aut_label': '8E1', 'centralizer': '3240.e1.a1', 'counter': 26, 'group_counter': 70, 'group_order': 51840, 'label': '8E1', 'order': 8, 'powers': [10, 27, 26], 'representative': 46397, 'size': 3240}
  • id: 163589942
    {'aut_label': '8E-1', 'centralizer': '3240.e1.a1', 'counter': 27, 'group_counter': 70, 'group_order': 51840, 'label': '8E-1', 'order': 8, 'powers': [10, 26, 27], 'representative': 36911, 'size': 3240}
  • id: 163589943
    {'aut_label': '8E1', 'centralizer': '3240.e1.a1', 'counter': 28, 'group_counter': 70, 'group_order': 51840, 'label': '8F1', 'order': 8, 'powers': [10, 29, 28], 'representative': 22261, 'size': 3240}
  • id: 163589944
    {'aut_label': '8E-1', 'centralizer': '3240.e1.a1', 'counter': 29, 'group_counter': 70, 'group_order': 51840, 'label': '8F-1', 'order': 8, 'powers': [10, 28, 29], 'representative': 4423, 'size': 3240}
  • id: 163589946
    {'aut_label': '10A', 'centralizer': '324.d1.a1', 'counter': 30, 'group_counter': 70, 'group_order': 51840, 'label': '10A', 'order': 10, 'powers': [16, 30, 3], 'representative': 25568, 'size': 324}
  • id: 163589947
    {'aut_label': '10B', 'centralizer': '324.d1.a1', 'counter': 31, 'group_counter': 70, 'group_order': 51840, 'label': '10B', 'order': 10, 'powers': [16, 31, 2], 'representative': 20864, 'size': 324}
  • id: 163589948
    {'aut_label': '10C', 'centralizer': '324.d1.a1', 'counter': 32, 'group_counter': 70, 'group_order': 51840, 'label': '10C', 'order': 10, 'powers': [16, 32, 4], 'representative': 20896, 'size': 324}
  • id: 163589949
    {'aut_label': '12A1', 'centralizer': '2160.b1.a1', 'counter': 33, 'group_counter': 70, 'group_order': 51840, 'label': '12A1', 'order': 12, 'powers': [18, 12, 33], 'representative': 2683, 'size': 2160}
  • id: 163589950
    {'aut_label': '12A-1', 'centralizer': '2160.b1.a1', 'counter': 34, 'group_counter': 70, 'group_order': 51840, 'label': '12A-1', 'order': 12, 'powers': [18, 13, 34], 'representative': 1561, 'size': 2160}
  • id: 163589951
    {'aut_label': '12A1', 'centralizer': '2160.b1.a1', 'counter': 35, 'group_counter': 70, 'group_order': 51840, 'label': '12B1', 'order': 12, 'powers': [18, 14, 35], 'representative': 26251, 'size': 2160}
  • id: 163589952
    {'aut_label': '12A-1', 'centralizer': '2160.b1.a1', 'counter': 36, 'group_counter': 70, 'group_order': 51840, 'label': '12B-1', 'order': 12, 'powers': [18, 15, 36], 'representative': 5417, 'size': 2160}
  • id: 163589953
    {'aut_label': '16A1', 'centralizer': '324.d1.a1', 'counter': 37, 'group_counter': 70, 'group_order': 51840, 'label': '16A1', 'order': 16, 'powers': [20, 37, 38], 'representative': 30900, 'size': 324}
  • id: 163589954
    {'aut_label': '16A-1', 'centralizer': '324.d1.a1', 'counter': 38, 'group_counter': 70, 'group_order': 51840, 'label': '16A-1', 'order': 16, 'powers': [21, 38, 37], 'representative': 25740, 'size': 324}
  • id: 163589955
    {'aut_label': '16A1', 'centralizer': '324.d1.a1', 'counter': 39, 'group_counter': 70, 'group_order': 51840, 'label': '16B1', 'order': 16, 'powers': [20, 39, 40], 'representative': 3100, 'size': 324}
  • id: 163589957
    {'aut_label': '16A-1', 'centralizer': '324.d1.a1', 'counter': 40, 'group_counter': 70, 'group_order': 51840, 'label': '16B-1', 'order': 16, 'powers': [21, 40, 39], 'representative': 39780, 'size': 324}
  • id: 163589958
    {'aut_label': '16C1', 'centralizer': '1620.e1.a1', 'counter': 41, 'group_counter': 70, 'group_order': 51840, 'label': '16C1', 'order': 16, 'powers': [20, 41, 42], 'representative': 32046, 'size': 1620}
  • id: 163589959
    {'aut_label': '16C-1', 'centralizer': '1620.e1.a1', 'counter': 42, 'group_counter': 70, 'group_order': 51840, 'label': '16C-1', 'order': 16, 'powers': [21, 42, 41], 'representative': 45686, 'size': 1620}
  • id: 163589960
    {'aut_label': '16C1', 'centralizer': '1620.e1.a1', 'counter': 43, 'group_counter': 70, 'group_order': 51840, 'label': '16D1', 'order': 16, 'powers': [20, 43, 44], 'representative': 6638, 'size': 1620}
  • id: 163589961
    {'aut_label': '16C-1', 'centralizer': '1620.e1.a1', 'counter': 44, 'group_counter': 70, 'group_order': 51840, 'label': '16D-1', 'order': 16, 'powers': [21, 44, 43], 'representative': 29558, 'size': 1620}
  • id: 163589962
    {'aut_label': '20A1', 'centralizer': '324.d1.a1', 'counter': 45, 'group_counter': 70, 'group_order': 51840, 'label': '20A1', 'order': 20, 'powers': [30, 45, 9], 'representative': 4944, 'size': 324}
  • id: 163589963
    {'aut_label': '20A-1', 'centralizer': '324.d1.a1', 'counter': 46, 'group_counter': 70, 'group_order': 51840, 'label': '20A-1', 'order': 20, 'powers': [30, 46, 9], 'representative': 39536, 'size': 324}
  • id: 163589964
    {'aut_label': '20B1', 'centralizer': '324.d1.a1', 'counter': 47, 'group_counter': 70, 'group_order': 51840, 'label': '20B1', 'order': 20, 'powers': [30, 47, 8], 'representative': 2576, 'size': 324}
  • id: 163589965
    {'aut_label': '20B-1', 'centralizer': '324.d1.a1', 'counter': 48, 'group_counter': 70, 'group_order': 51840, 'label': '20B-1', 'order': 20, 'powers': [30, 48, 8], 'representative': 24944, 'size': 324}
  • id: 163589966
    {'aut_label': '40A1', 'centralizer': '324.d1.a1', 'counter': 49, 'group_counter': 70, 'group_order': 51840, 'label': '40A1', 'order': 40, 'powers': [47, 49, 20], 'representative': 29128, 'size': 324}
  • id: 163589968
    {'aut_label': '40A-1', 'centralizer': '324.d1.a1', 'counter': 50, 'group_counter': 70, 'group_order': 51840, 'label': '40A-1', 'order': 40, 'powers': [48, 50, 21], 'representative': 12472, 'size': 324}
  • id: 163589969
    {'aut_label': '40A7', 'centralizer': '324.d1.a1', 'counter': 51, 'group_counter': 70, 'group_order': 51840, 'label': '40A7', 'order': 40, 'powers': [47, 51, 21], 'representative': 1976, 'size': 324}
  • id: 163589970
    {'aut_label': '40A-7', 'centralizer': '324.d1.a1', 'counter': 52, 'group_counter': 70, 'group_order': 51840, 'label': '40A-7', 'order': 40, 'powers': [48, 52, 20], 'representative': 41544, 'size': 324}
  • id: 163589971
    {'aut_label': '40B1', 'centralizer': '324.d1.a1', 'counter': 53, 'group_counter': 70, 'group_order': 51840, 'label': '40B1', 'order': 40, 'powers': [48, 53, 22], 'representative': 27352, 'size': 324}
  • id: 163589972
    {'aut_label': '40B-1', 'centralizer': '324.d1.a1', 'counter': 54, 'group_counter': 70, 'group_order': 51840, 'label': '40B-1', 'order': 40, 'powers': [47, 54, 23], 'representative': 31848, 'size': 324}
  • id: 163589973
    {'aut_label': '40B7', 'centralizer': '324.d1.a1', 'counter': 55, 'group_counter': 70, 'group_order': 51840, 'label': '40B7', 'order': 40, 'powers': [48, 55, 23], 'representative': 50984, 'size': 324}
  • id: 163589974
    {'aut_label': '40B-7', 'centralizer': '324.d1.a1', 'counter': 56, 'group_counter': 70, 'group_order': 51840, 'label': '40B-7', 'order': 40, 'powers': [47, 56, 22], 'representative': 44376, 'size': 324}
  • id: 163589975
    {'aut_label': '80A1', 'centralizer': '324.d1.a1', 'counter': 57, 'group_counter': 70, 'group_order': 51840, 'label': '80A1', 'order': 80, 'powers': [49, 57, 37], 'representative': 42404, 'size': 324}
  • id: 163589976
    {'aut_label': '80A-1', 'centralizer': '324.d1.a1', 'counter': 58, 'group_counter': 70, 'group_order': 51840, 'label': '80A-1', 'order': 80, 'powers': [50, 58, 38], 'representative': 5916, 'size': 324}
  • id: 163589977
    {'aut_label': '80A7', 'centralizer': '324.d1.a1', 'counter': 59, 'group_counter': 70, 'group_order': 51840, 'label': '80A7', 'order': 80, 'powers': [51, 59, 38], 'representative': 48188, 'size': 324}
  • id: 163589979
    {'aut_label': '80A-7', 'centralizer': '324.d1.a1', 'counter': 60, 'group_counter': 70, 'group_order': 51840, 'label': '80A-7', 'order': 80, 'powers': [52, 60, 37], 'representative': 47812, 'size': 324}
  • id: 163589980
    {'aut_label': '80A11', 'centralizer': '324.d1.a1', 'counter': 61, 'group_counter': 70, 'group_order': 51840, 'label': '80A11', 'order': 80, 'powers': [52, 61, 37], 'representative': 46284, 'size': 324}
  • id: 163589981
    {'aut_label': '80A-11', 'centralizer': '324.d1.a1', 'counter': 62, 'group_counter': 70, 'group_order': 51840, 'label': '80A-11', 'order': 80, 'powers': [51, 62, 38], 'representative': 13556, 'size': 324}
  • id: 163589982
    {'aut_label': '80A13', 'centralizer': '324.d1.a1', 'counter': 63, 'group_counter': 70, 'group_order': 51840, 'label': '80A13', 'order': 80, 'powers': [50, 63, 38], 'representative': 1492, 'size': 324}
  • id: 163589983
    {'aut_label': '80A-13', 'centralizer': '324.d1.a1', 'counter': 64, 'group_counter': 70, 'group_order': 51840, 'label': '80A-13', 'order': 80, 'powers': [49, 64, 37], 'representative': 24428, 'size': 324}
  • id: 163589984
    {'aut_label': '80A11', 'centralizer': '324.d1.a1', 'counter': 65, 'group_counter': 70, 'group_order': 51840, 'label': '80B1', 'order': 80, 'powers': [52, 65, 39], 'representative': 38316, 'size': 324}
  • id: 163589985
    {'aut_label': '80A-11', 'centralizer': '324.d1.a1', 'counter': 66, 'group_counter': 70, 'group_order': 51840, 'label': '80B-1', 'order': 80, 'powers': [51, 66, 40], 'representative': 51284, 'size': 324}
  • id: 163589986
    {'aut_label': '80A-1', 'centralizer': '324.d1.a1', 'counter': 67, 'group_counter': 70, 'group_order': 51840, 'label': '80B7', 'order': 80, 'powers': [50, 67, 40], 'representative': 22132, 'size': 324}
  • id: 163589987
    {'aut_label': '80A1', 'centralizer': '324.d1.a1', 'counter': 68, 'group_counter': 70, 'group_order': 51840, 'label': '80B-7', 'order': 80, 'powers': [49, 68, 39], 'representative': 5068, 'size': 324}
  • id: 163589988
    {'aut_label': '80A-13', 'centralizer': '324.d1.a1', 'counter': 69, 'group_counter': 70, 'group_order': 51840, 'label': '80B11', 'order': 80, 'powers': [49, 69, 39], 'representative': 10916, 'size': 324}
  • id: 163589990
    {'aut_label': '80A13', 'centralizer': '324.d1.a1', 'counter': 70, 'group_counter': 70, 'group_order': 51840, 'label': '80B-11', 'order': 80, 'powers': [50, 70, 40], 'representative': 49884, 'size': 324}
  • id: 163589991
    {'aut_label': '80A7', 'centralizer': '324.d1.a1', 'counter': 71, 'group_counter': 70, 'group_order': 51840, 'label': '80B13', 'order': 80, 'powers': [51, 71, 40], 'representative': 14908, 'size': 324}
  • id: 163589992
    {'aut_label': '80A-7', 'centralizer': '324.d1.a1', 'counter': 72, 'group_counter': 70, 'group_order': 51840, 'label': '80B-13', 'order': 80, 'powers': [52, 72, 39], 'representative': 9732, 'size': 324}
• 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: 16340367
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16340378
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, -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, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 16340389
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, -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, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 16340399
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, -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, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 16340400
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, -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, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
  • id: 16340401
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16340402
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16340403
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.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, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16340404
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, -2], 'schur_index': 1}
  • id: 16340368
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 2, -2, 2, 2, 2, -2, -2, 2], 'schur_index': 1}
  • id: 16340369
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 16340370
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 16340371
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340372
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340373
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2c', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 16340374
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2d', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 16340375
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2e', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340376
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2f', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, 0, 0, 0, 0, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340377
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2g', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340379
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.2h', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340380
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, -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: 16340381
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4b', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, -4, -4, 4, 4, 0, 0, 0, 0, 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: 16340382
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4c', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, -1, -4, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 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: 16340383
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4d', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, -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: 16340384
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4e', 'multiplicity': 2, 'nt': [16, 136], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340385
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4f', 'multiplicity': 2, 'nt': [16, 136], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340386
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4g', 'multiplicity': 2, 'nt': [20, 18], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, -2, -8, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340387
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4h', 'multiplicity': 2, 'nt': [20, 18], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, -2, 8, 0, 0, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340388
    {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4i', 'multiplicity': 4, 'nt': [40, 124], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 16, -16, 16, 0, 0, 0, 0, 0, 0, -4, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340390
    {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4j', 'multiplicity': 4, 'nt': [40, 124], 'qdim': 16, 'qvalues': [16, 16, 16, 16, 0, 0, 16, -16, -16, 0, 0, 0, 0, 0, 0, -4, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340391
    {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4k', 'multiplicity': 8, 'nt': [80, 0], 'qdim': 32, 'qvalues': [32, -32, -32, 32, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, -8, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340392
    {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.4l', 'multiplicity': 8, 'nt': [80, 0], 'qdim': 32, 'qvalues': [32, 32, -32, -32, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, -8, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340393
    {'cdim': 80, 'counter': 33, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.80a', 'multiplicity': 1, 'nt': [81, 0], 'qdim': 80, 'qvalues': [80, 80, 0, 0, 8, 8, -1, 0, 0, 0, 0, 2, 2, 2, 2, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340394
    {'cdim': 80, 'counter': 34, 'faithful': True, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.80b', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 80, 'qvalues': [80, -80, 0, 0, 8, -8, -1, 0, 0, 0, 0, -2, -2, 2, 2, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340395
    {'cdim': 80, 'counter': 35, 'faithful': True, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.80c', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 80, 'qvalues': [80, -80, 0, 0, 8, -8, -1, 0, 0, 0, 0, 2, 2, -2, -2, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340396
    {'cdim': 80, 'counter': 36, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.80d', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 80, 'qvalues': [80, 80, 0, 0, 8, 8, -1, 0, 0, 0, 0, -2, -2, -2, -2, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340397
    {'cdim': 80, 'counter': 37, 'faithful': True, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.80e', 'multiplicity': 2, 'nt': [324, 0], 'qdim': 160, 'qvalues': [160, -160, 0, 0, -16, 16, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16340398
    {'cdim': 80, 'counter': 38, 'faithful': False, 'group': '51840.cr', 'group_order': 51840, 'image': None, 'label': '51840.cr.80f', 'multiplicity': 2, 'nt': [324, 0], 'qdim': 160, 'qvalues': [160, 160, 0, 0, -16, -16, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 36464986
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 51840, 'label': '51840.cr.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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 36464997
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.d1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 36465008
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.c1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36465019
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36465030
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 36465041
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 36465052
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36465056
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 25920, 'label': '51840.cr.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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36465057
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.a1', 'kernel_order': 12960, 'label': '51840.cr.1i1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 36464987
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.a1', 'kernel_order': 12960, 'label': '51840.cr.1i2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 36464988
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.b1', 'kernel_order': 12960, 'label': '51840.cr.1j1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36464989
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.g1.b1', 'kernel_order': 12960, 'label': '51840.cr.1j2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36464990
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 12960, 'label': '51840.cr.1k1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36464991
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 12960, 'label': '51840.cr.1k2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36464992
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 12960, 'label': '51840.cr.1l1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 36464993
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 51840, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 12960, 'label': '51840.cr.1l2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 36464994
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 12960, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 6480, 'label': '51840.cr.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36464995
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 12960, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 6480, 'label': '51840.cr.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36464996
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 12960, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.g1.a1', 'kernel_order': 6480, 'label': '51840.cr.2c', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36464998
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 12960, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.c1.a1', 'kernel_order': 6480, 'label': '51840.cr.2d', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36464999
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.g1.a1', 'kernel_order': 3240, 'label': '51840.cr.2e1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36465000
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.g1.a1', 'kernel_order': 3240, 'label': '51840.cr.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36465001
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 23, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.e1.a1', 'kernel_order': 3240, 'label': '51840.cr.2f1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
  • id: 36465002
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 24, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.e1.a1', 'kernel_order': 3240, 'label': '51840.cr.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36465003
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 25, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 3240, 'label': '51840.cr.2g1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]]]}
  • id: 36465004
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 26, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 3240, 'label': '51840.cr.2g2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36465005
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 27, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3240, 'label': '51840.cr.2h1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]]]}
  • id: 36465006
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 6480, 'counter': 28, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 3240, 'label': '51840.cr.2h2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]]]}
  • id: 36465007
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 2592, 'counter': 29, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 2592, 'label': '51840.cr.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 36465009
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 2592, 'counter': 30, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.a1', 'kernel_order': 1296, 'label': '51840.cr.4b', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-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: 36465010
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 2592, 'counter': 31, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.b1.b1', 'kernel_order': 1296, 'label': '51840.cr.4c', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 36465011
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 2592, 'counter': 32, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1.a1', 'kernel_order': 1296, 'label': '51840.cr.4d', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 36465012
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 1620, 'counter': 33, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '64.46', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.a1', 'kernel_order': 810, 'label': '51840.cr.4e1', 'nt': [16, 136], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465013
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 1620, 'counter': 34, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '64.46', 'image_order': 64, 'indicator': 0, 'kernel': '64.c1.a1', 'kernel_order': 810, 'label': '51840.cr.4e2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465014
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 1620, 'counter': 35, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '64.46', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 810, 'label': '51840.cr.4f1', 'nt': [16, 136], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465015
    {'center': '32.a1.a1', 'center_index': 32, 'center_order': 1620, 'counter': 36, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '64.46', 'image_order': 64, 'indicator': 0, 'kernel': '64.a1.a1', 'kernel_order': 810, 'label': '51840.cr.4f2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465016
    {'center': '40.a1.a1', 'center_index': 40, 'center_order': 1296, 'counter': 37, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '80.31', 'image_order': 80, 'indicator': 0, 'kernel': '80.c1.a1', 'kernel_order': 648, 'label': '51840.cr.4g1', 'nt': [20, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]]]}
  • id: 36465017
    {'center': '40.a1.a1', 'center_index': 40, 'center_order': 1296, 'counter': 38, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '80.31', 'image_order': 80, 'indicator': 0, 'kernel': '80.c1.a1', 'kernel_order': 648, 'label': '51840.cr.4g2', 'nt': [20, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]]]}
  • id: 36465018
    {'center': '40.a1.a1', 'center_index': 40, 'center_order': 1296, 'counter': 39, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '80.31', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 648, 'label': '51840.cr.4h1', 'nt': [20, 18], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]]]}
  • id: 36465020
    {'center': '40.a1.a1', 'center_index': 40, 'center_order': 1296, 'counter': 40, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [5, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '80.31', 'image_order': 80, 'indicator': 0, 'kernel': '80.a1.a1', 'kernel_order': 648, 'label': '51840.cr.4h2', 'nt': [20, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]]]}
  • id: 36465021
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 41, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 324, 'label': '51840.cr.4i1', 'nt': [40, 124], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]]]}
  • id: 36465022
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 42, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 324, 'label': '51840.cr.4i2', 'nt': [40, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]]]}
  • id: 36465023
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 43, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 324, 'label': '51840.cr.4i3', 'nt': [40, 124], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]]]}
  • id: 36465024
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 44, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 324, 'label': '51840.cr.4i4', 'nt': [40, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]]]}
  • id: 36465025
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 45, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.a1.a1', 'kernel_order': 324, 'label': '51840.cr.4j1', 'nt': [40, 124], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[2, 6], [-1, 10], [2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]]]}
  • id: 36465026
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 46, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.a1.a1', 'kernel_order': 324, 'label': '51840.cr.4j2', 'nt': [40, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]]]}
  • id: 36465027
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 47, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.a1.a1', 'kernel_order': 324, 'label': '51840.cr.4j3', 'nt': [40, 124], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]]]}
  • id: 36465028
    {'center': '80.a1.a1', 'center_index': 80, 'center_order': 648, 'counter': 48, 'cyclotomic_n': 40, 'dim': 4, 'faithful': False, 'field': [9, 0, -4, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '160.68', 'image_order': 160, 'indicator': 0, 'kernel': '160.a1.a1', 'kernel_order': 324, 'label': '51840.cr.4j4', 'nt': [40, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[2, 6], [-1, 10], [2, 14]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]]]}
  • id: 36465029
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 49, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k1', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]]]}
  • id: 36465031
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 50, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k2', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]]]}
  • id: 36465032
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 51, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k3', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]]]}
  • id: 36465033
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 52, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k4', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]]]}
  • id: 36465034
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 53, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k5', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]]]}
  • id: 36465035
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 54, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k6', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]]]}
  • id: 36465036
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 55, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k7', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]]]}
  • id: 36465037
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 56, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.c1.a1', 'kernel_order': 162, 'label': '51840.cr.4k8', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]]]}
  • id: 36465038
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 57, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l1', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]]]}
  • id: 36465039
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 58, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l2', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]]]}
  • id: 36465040
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 59, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l3', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]]]}
  • id: 36465042
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 60, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l4', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]]]}
  • id: 36465043
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 61, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l5', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]]]}
  • id: 36465044
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 62, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l6', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]]]}
  • id: 36465045
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 63, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l7', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]]]}
  • id: 36465046
    {'center': '160.a1.a1', 'center_index': 160, 'center_order': 324, 'counter': 64, 'cyclotomic_n': 80, 'dim': 4, 'faithful': False, 'field': [225, 0, 200, 0, 60, 0, 0, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '320.186', 'image_order': 320, 'indicator': 0, 'kernel': '320.a1.a1', 'kernel_order': 162, 'label': '51840.cr.4l8', 'nt': [80, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 10], [2, 30]], [[-2, 10], [-2, 30]], [[-2, 10], [-2, 30]], [[2, 10], [2, 30]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[-2, 12], [1, 20], [-2, 28]], [[2, 12], [-1, 20], [2, 28]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 10], [1, 14], [-1, 18], [1, 30]], [[-1, 2], [-1, 6], [1, 14], [-1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 14], [1, 18]], [[1, 2], [1, 6], [-1, 10], [-1, 14], [1, 18], [-1, 30]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [-1, 9], [-1, 11], [2, 17], [-1, 19], [-1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 1], [1, 9], [1, 11], [-2, 17], [1, 19], [1, 25]], [[-1, 7], [-1, 21], [1, 23], [-1, 29]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[1, 1], [1, 3], [1, 9], [1, 27]], [[-1, 1], [-1, 3], [-1, 9], [-1, 27]], [[1, 5], [1, 7], [-2, 13], [-1, 15], [1, 21], [1, 23], [-1, 29], [-2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]], [[-1, 5], [-1, 7], [2, 13], [1, 15], [-1, 21], [-1, 23], [1, 29], [2, 31]], [[1, 7], [1, 21], [-1, 23], [1, 29]]]}
  • id: 36465047
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 65, 'cyclotomic_n': 1, 'dim': 80, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '25920.dn', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1.a1', 'kernel_order': 2, 'label': '51840.cr.80a', 'nt': [81, 0], 'q_character': None, 'values': [[[80, 0]], [[80, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465048
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 66, 'cyclotomic_n': 1, 'dim': 80, 'faithful': True, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '51840.cr', 'image_order': 51840, 'indicator': 1, 'kernel': '51840.a1.a1', 'kernel_order': 1, 'label': '51840.cr.80b', 'nt': [162, 0], 'q_character': None, 'values': [[[80, 0]], [[-80, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465049
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 67, 'cyclotomic_n': 1, 'dim': 80, 'faithful': True, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '51840.cr', 'image_order': 51840, 'indicator': 1, 'kernel': '51840.a1.a1', 'kernel_order': 1, 'label': '51840.cr.80c', 'nt': [162, 0], 'q_character': None, 'values': [[[80, 0]], [[-80, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465050
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 68, 'cyclotomic_n': 1, 'dim': 80, 'faithful': False, 'field': [0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '25920.dn', 'image_order': 25920, 'indicator': 1, 'kernel': '25920.a1.a1', 'kernel_order': 2, 'label': '51840.cr.80d', 'nt': [162, 0], 'q_character': None, 'values': [[[80, 0]], [[80, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465051
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 69, 'cyclotomic_n': 4, 'dim': 80, 'faithful': True, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '51840.cr', 'image_order': 51840, 'indicator': 0, 'kernel': '51840.a1.a1', 'kernel_order': 1, 'label': '51840.cr.80e1', 'nt': [324, 0], 'q_character': None, 'values': [[[80, 0]], [[-80, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465053
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 70, 'cyclotomic_n': 4, 'dim': 80, 'faithful': True, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '51840.cr', 'image_order': 51840, 'indicator': 0, 'kernel': '51840.a1.a1', 'kernel_order': 1, 'label': '51840.cr.80e2', 'nt': [324, 2], 'q_character': None, 'values': [[[80, 0]], [[-80, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465054
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 71, 'cyclotomic_n': 4, 'dim': 80, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '25920.dn', 'image_order': 25920, 'indicator': 0, 'kernel': '25920.a1.a1', 'kernel_order': 2, 'label': '51840.cr.80f1', 'nt': [324, 0], 'q_character': None, 'values': [[[80, 0]], [[80, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36465055
    {'center': '25920.a1.a1', 'center_index': 25920, 'center_order': 2, 'counter': 72, 'cyclotomic_n': 4, 'dim': 80, 'faithful': False, 'field': [1, 0, 1], 'group': '51840.cr', 'group_counter': 70, 'group_order': 51840, 'image': None, 'image_isoclass': '25920.dn', 'image_order': 25920, 'indicator': 0, 'kernel': '25920.a1.a1', 'kernel_order': 2, 'label': '51840.cr.80f2', 'nt': [324, 2], 'q_character': None, 'values': [[[80, 0]], [[80, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 223462009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 51840, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '51840.cr.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '51840.cr', 'subgroup_hash': 8363559991699411848, 'subgroup_order': 51840, 'subgroup_tex': 'C_2\\times F_{81}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 25920, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '25920.dm', 'subgroup_hash': 7772596281349664310, 'subgroup_order': 25920, 'subgroup_tex': 'C_3^4:D_{10}.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 25920, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3661836073757997727, 'subgroup_order': 25920, 'subgroup_tex': 'C_2\\times C_3^4.(C_8.F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 25920, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8566089708495429302, 'subgroup_order': 25920, 'subgroup_tex': 'C_2\\times C_3^4.C_{80}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462404
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 25920, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '51840.cr.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, '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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25920.dn', 'subgroup_hash': 1549518908401167474, 'subgroup_order': 25920, 'subgroup_tex': 'F_{81}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 25920, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '51840.cr.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.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': '25920.dn', 'subgroup_hash': 1549518908401167474, 'subgroup_order': 25920, 'subgroup_tex': 'F_{81}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 25920, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '51840.cr.2.d1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.c1', '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': '25920.dn', 'subgroup_hash': 1549518908401167474, 'subgroup_order': 25920, 'subgroup_tex': 'F_{81}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 25920, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '51840.cr.2.d1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.d1', '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': '25920.dn', 'subgroup_hash': 1549518908401167474, 'subgroup_order': 25920, 'subgroup_tex': 'F_{81}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 12960, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4263613368376032045, 'subgroup_order': 12960, 'subgroup_tex': 'C_2\\times C_3^4.(C_8\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 12960, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12960.a', 'subgroup_hash': 8347927909691576433, 'subgroup_order': 12960, 'subgroup_tex': 'C_2\\times F_{81}', 'supersolvable': False, 'sylow': 0}
  • id: 223462021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 12960, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4230886542335322205, 'subgroup_order': 12960, 'subgroup_tex': 'C_2\\times C_3^4.C_{40}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12960.bx', 'subgroup_hash': 6161210740019565112, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4:C_{40}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '12960.bx', 'subgroup_hash': 6161210740019565112, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4:C_{40}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5176448573704742448, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.(C_8.F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5176448573704742448, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.(C_8.F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1606518578507326774, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.C_{80}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1606518578507326774, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.C_{80}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1606518578507326774, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.C_{80}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12960, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.4.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1606518578507326774, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.C_{80}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 1657717120232051862, 'subgroup_order': 12960, 'subgroup_tex': 'C_2\\times C_3^4.D_5.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 2429053582589769169, 'subgroup_order': 12960, 'subgroup_tex': 'C_2\\times C_3^4:C_5.\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12960.bx', 'subgroup_hash': 6161210740019565112, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4:C_{40}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5176448573704742448, 'subgroup_order': 12960, 'subgroup_tex': 'C_3^4.(C_8.F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2592, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '51840.cr.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10368.oy', 'subgroup_hash': 4648268705809218033, 'subgroup_order': 10368, 'subgroup_tex': 'C_3^4:\\OD_{32}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7501035513648911927, 'subgroup_order': 6480, 'subgroup_tex': 'C_2\\times C_3^4.D_{10}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6480.g', 'subgroup_hash': 4561320303876548379, 'subgroup_order': 6480, 'subgroup_tex': 'C_2\\times C_3^4:C_{40}', 'supersolvable': False, 'sylow': 0}
  • id: 223462198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1150918008722405077, 'subgroup_order': 6480, 'subgroup_tex': 'C_2\\times C_3^4:C_5.C_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.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': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6480.cp', 'subgroup_hash': 3977776343620020028, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:(C_8\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '6480.cp', 'subgroup_hash': 3977776343620020028, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:(C_8\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6480.cp', 'subgroup_hash': 3977776343620020028, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:(C_8\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462243
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 6480, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6480.cp', 'subgroup_hash': 3977776343620020028, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:(C_8\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6480.a', 'subgroup_hash': 3860183301578138941, 'subgroup_order': 6480, 'subgroup_tex': 'F_{81}', 'supersolvable': False, 'sylow': 0}
  • id: 223462265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6480.a', 'subgroup_hash': 3860183301578138941, 'subgroup_order': 6480, 'subgroup_tex': 'F_{81}', 'supersolvable': False, 'sylow': 0}
  • id: 223462276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3709942671132945375, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4.C_{40}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6480, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3709942671132945375, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4.C_{40}.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 223462298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6480.bo', 'subgroup_hash': 6953428835306623246, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:(C_2^2\\times F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 42681221920932071, 'subgroup_order': 6480, 'subgroup_tex': 'C_2\\times C_3^4:C_5.C_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6480.bm', 'subgroup_hash': 6378546528877111736, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:C_{20}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.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': '6480.bm', 'subgroup_hash': 6378546528877111736, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:C_{20}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 6347978062242817124, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:C_5.\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.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': None, 'subgroup_hash': 6347978062242817124, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:C_5.\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6480.bm', 'subgroup_hash': 6378546528877111736, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:C_{20}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3240, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 6347978062242817124, 'subgroup_order': 6480, 'subgroup_tex': 'C_3^4:C_5.\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8499642411294132704, 'subgroup_order': 5184, 'subgroup_tex': 'C_2\\times C_3^4.C_8:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462398
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ns', 'subgroup_hash': 5126350881959894628, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^4:C_2^3.Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2592, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.mf', 'subgroup_hash': 3256735746113916699, 'subgroup_order': 5184, 'subgroup_tex': 'C_2\\times C_3^4:\\OD_{32}', 'supersolvable': False, 'sylow': 0}
  • id: 223462401
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ce', 'subgroup_hash': 1854156772860425011, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^4:C_{16}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ce', 'subgroup_hash': 1854156772860425011, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^4:C_{16}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ce', 'subgroup_hash': 1854156772860425011, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^4:C_{16}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462405
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.10.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.d1.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ce', 'subgroup_hash': 1854156772860425011, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^4:C_{16}:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bg', 'subgroup_hash': 6380495160886074933, 'subgroup_order': 3240, 'subgroup_tex': 'C_2\\times C_3^4:D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.f', 'subgroup_hash': 6474031154872375343, 'subgroup_order': 3240, 'subgroup_tex': 'C_2\\times C_3^4:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 223462408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6868738007427824758, 'subgroup_order': 3240, 'subgroup_tex': 'C_2\\times C_3^4:(C_5:C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 223462409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.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': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bh', 'subgroup_hash': 2057178933574772344, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_4\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bh', 'subgroup_hash': 2057178933574772344, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_4\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bh', 'subgroup_hash': 2057178933574772344, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_4\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bh', 'subgroup_hash': 2057178933574772344, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_4\\times D_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.b', 'subgroup_hash': 4099259894179074105, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_{40}', 'supersolvable': False, 'sylow': 0}
  • id: 223462414
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.b', 'subgroup_hash': 4099259894179074105, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_{40}', 'supersolvable': False, 'sylow': 0}
  • id: 223462416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.ce', 'subgroup_hash': 4769609222358653251, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_5:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 3240, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3240.ce', 'subgroup_hash': 4769609222358653251, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_5:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 810, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.bf', 'subgroup_hash': 7636397916644946565, 'subgroup_order': 3240, 'subgroup_tex': 'C_2\\times C_3^4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 223462419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1620, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.be', 'subgroup_hash': 2701722344868570601, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_2\\times F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1620, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.be', 'subgroup_hash': 2701722344868570601, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_2\\times F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1620, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.cf', 'subgroup_hash': 6807394357865232183, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_5:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1620, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.16.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.cf', 'subgroup_hash': 6807394357865232183, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_5:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 810, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3240.be', 'subgroup_hash': 2701722344868570601, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:(C_2\\times F_5)', 'supersolvable': False, 'sylow': 0}
  • id: 223462424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 2592, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.k', 'subgroup_hash': 154672268184796210, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_3^4:C_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1955321438404587138, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_3^4.C_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.jt', 'subgroup_hash': 8356414212655845248, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:(C_2^2\\times F_9)', 'supersolvable': False, 'sylow': 0}
  • id: 223462428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.fb', 'subgroup_hash': 2283064285231441539, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_3^4:\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.k', 'subgroup_hash': 154672268184796210, 'subgroup_order': 2592, 'subgroup_tex': 'C_2\\times C_3^4:C_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lt', 'subgroup_hash': 7248750283178589491, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2\\wr C_2.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lt', 'subgroup_hash': 7248750283178589491, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2\\wr C_2.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.lt', 'subgroup_hash': 7248750283178589491, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2\\wr C_2.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ct', 'subgroup_hash': 1515785214594576051, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:F_9.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ct', 'subgroup_hash': 1515785214594576051, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:F_9.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.co', 'subgroup_hash': 8938496937969911657, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:\\OD_{32}', 'supersolvable': False, 'sylow': 0}
  • id: 223462436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.co', 'subgroup_hash': 8938496937969911657, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:\\OD_{32}', 'supersolvable': False, 'sylow': 0}
  • id: 223462438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ct', 'subgroup_hash': 1515785214594576051, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:F_9.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.co', 'subgroup_hash': 8938496937969911657, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:\\OD_{32}', 'supersolvable': False, 'sylow': 0}
  • id: 223462440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.20.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.co', 'subgroup_hash': 8938496937969911657, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:\\OD_{32}', 'supersolvable': False, 'sylow': 0}
  • id: 223462441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.425', 'subgroup_hash': 425, 'subgroup_order': 1620, 'subgroup_tex': 'C_2\\times C_3^4:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.422', 'subgroup_hash': 422, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.422', 'subgroup_hash': 422, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.420', 'subgroup_hash': 420, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 223462445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.420', 'subgroup_hash': 420, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:C_{20}', 'supersolvable': False, 'sylow': 0}
  • id: 223462446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.419', 'subgroup_hash': 419, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:C_5:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1620, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1620.419', 'subgroup_hash': 419, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:C_5:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 810, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1620.424', 'subgroup_hash': 424, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 810, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1620.422', 'subgroup_hash': 422, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:D_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 405, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1620.421', 'subgroup_hash': 421, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 223462452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 405, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.32.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1620.421', 'subgroup_hash': 421, 'subgroup_order': 1620, 'subgroup_tex': 'C_3^4:F_5', 'supersolvable': False, 'sylow': 0}
  • id: 223462453
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1296, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3561', 'subgroup_hash': 3561, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462454
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3495', 'subgroup_hash': 3495, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462455
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.40.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3495', 'subgroup_hash': 3495, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3568', 'subgroup_hash': 3568, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:(C_2^2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 223462457
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3567', 'subgroup_hash': 3567, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:(C_4\\times D_6)', 'supersolvable': False, 'sylow': 0}
  • id: 223462458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3562', 'subgroup_hash': 3562, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3562', 'subgroup_hash': 3562, 'subgroup_order': 1296, 'subgroup_tex': 'C_2\\times C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3499', 'subgroup_hash': 3499, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3499', 'subgroup_hash': 3499, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3506', 'subgroup_hash': 3506, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:(C_2\\times F_9)', 'supersolvable': False, 'sylow': 0}
  • id: 223462015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3506', 'subgroup_hash': 3506, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:(C_2\\times F_9)', 'supersolvable': False, 'sylow': 0}
  • id: 223462016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3508', 'subgroup_hash': 3508, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3508', 'subgroup_hash': 3508, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3499', 'subgroup_hash': 3499, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3506', 'subgroup_hash': 3506, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:(C_2\\times F_9)', 'supersolvable': False, 'sylow': 0}
  • id: 223462020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3506', 'subgroup_hash': 3506, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:(C_2\\times F_9)', 'supersolvable': False, 'sylow': 0}
  • id: 223462022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3508', 'subgroup_hash': 3508, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3495', 'subgroup_hash': 3495, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.40.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3495', 'subgroup_hash': 3495, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 810, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '810.103', 'subgroup_hash': 103, 'subgroup_order': 810, 'subgroup_tex': 'C_3^4:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 810, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.106', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 106, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.D_4', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '810.102', 'subgroup_hash': 102, 'subgroup_order': 810, 'subgroup_tex': 'C_3^4:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 810, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '810.102', 'subgroup_hash': 102, 'subgroup_order': 810, 'subgroup_tex': 'C_3^4:C_{10}', 'supersolvable': False, 'sylow': 0}
  • id: 223462028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 405, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '810.101', 'subgroup_hash': 101, 'subgroup_order': 810, 'subgroup_tex': 'C_3^4:D_5', 'supersolvable': False, 'sylow': 0}
  • id: 223462029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 405, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.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': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '810.101', 'subgroup_hash': 101, 'subgroup_order': 810, 'subgroup_tex': 'C_3^4:D_5', 'supersolvable': False, 'sylow': 0}
  • id: 223462030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.745', 'subgroup_hash': 745, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.711', 'subgroup_hash': 711, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.711', 'subgroup_hash': 711, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.750', 'subgroup_hash': 750, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 223462035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.745', 'subgroup_hash': 745, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.743', 'subgroup_hash': 743, 'subgroup_order': 648, 'subgroup_tex': 'C_2\\times C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 223462038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 223462039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 223462040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 223462041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 223462042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 223462044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.712', 'subgroup_hash': 712, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.712', 'subgroup_hash': 712, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.712', 'subgroup_hash': 712, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.n1.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.712', 'subgroup_hash': 712, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.80.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 223462049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '51840.cr.81.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '640.6185', 'subgroup_hash': 6185, 'subgroup_order': 640, 'subgroup_tex': 'C_2\\times C_{40}:C_4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8296', 'subgroup_hash': 8296, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 223462051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
  • id: 223462052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 405, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 15, 'label': '51840.cr.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.886', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 886, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{32}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['L4', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '405.15', 'subgroup_hash': 15, 'subgroup_order': 405, 'subgroup_tex': 'C_3^4:C_5', 'supersolvable': False, 'sylow': 0}
  • id: 223462053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.68', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 68, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{40}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.175', 'subgroup_hash': 175, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '160.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.204', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 204, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '160.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.68', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 68, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{40}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.160.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.1057', 'subgroup_hash': 1057, 'subgroup_order': 320, 'subgroup_tex': 'D_{10}.\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.1060', 'subgroup_hash': 1060, 'subgroup_order': 320, 'subgroup_tex': 'C_2\\times C_{40}.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.527', 'subgroup_hash': 527, 'subgroup_order': 320, 'subgroup_tex': 'C_{16}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.186', 'subgroup_hash': 186, 'subgroup_order': 320, 'subgroup_tex': 'C_{80}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.186', 'subgroup_hash': 186, 'subgroup_order': 320, 'subgroup_tex': 'C_{80}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.d1.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.186', 'subgroup_hash': 186, 'subgroup_order': 320, 'subgroup_tex': 'C_{80}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.162.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.d1.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.186', 'subgroup_hash': 186, 'subgroup_order': 320, 'subgroup_tex': 'C_{80}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462073
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.882', 'subgroup_hash': 882, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.894', 'subgroup_hash': 894, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 223462075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1030', 'subgroup_hash': 1030, 'subgroup_order': 288, 'subgroup_tex': 'C_2^2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.843', 'subgroup_hash': 843, 'subgroup_order': 288, 'subgroup_tex': 'F_9:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.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': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.843', 'subgroup_hash': 843, 'subgroup_order': 288, 'subgroup_tex': 'F_9:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.843', 'subgroup_hash': 843, 'subgroup_order': 288, 'subgroup_tex': 'F_9:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.180.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.843', 'subgroup_hash': 843, 'subgroup_order': 288, 'subgroup_tex': 'F_9:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 223462083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 223462085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 223462086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 223462088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.240.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • id: 223462089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 171, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '320.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '320.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{80}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.55', 'subgroup_hash': 55, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 162, 'counter': 172, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '320.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '320.1057', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1057, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}.\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 162, 'counter': 173, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '51840.cr.320.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '320.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '320.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{80}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.320.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.320.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.204', 'subgroup_hash': 204, 'subgroup_order': 160, 'subgroup_tex': 'D_{10}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.120', 'subgroup_hash': 120, 'subgroup_order': 160, 'subgroup_tex': 'C_8\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.201', 'subgroup_hash': 201, 'subgroup_order': 160, 'subgroup_tex': 'C_{10}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.59', 'subgroup_hash': 59, 'subgroup_order': 160, 'subgroup_tex': 'C_2\\times C_{80}', 'supersolvable': True, 'sylow': 0}
  • id: 223462099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.18', 'subgroup_hash': 18, 'subgroup_order': 160, 'subgroup_tex': 'C_{10}:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.68', 'subgroup_hash': 68, 'subgroup_order': 160, 'subgroup_tex': 'C_{40}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.68', 'subgroup_hash': 68, 'subgroup_order': 160, 'subgroup_tex': 'C_{40}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.68', 'subgroup_hash': 68, 'subgroup_order': 160, 'subgroup_tex': 'C_{40}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.70', 'subgroup_hash': 70, 'subgroup_order': 160, 'subgroup_tex': 'C_{40}.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.70', 'subgroup_hash': 70, 'subgroup_order': 160, 'subgroup_tex': 'C_{40}.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.5', 'subgroup_hash': 5, 'subgroup_order': 160, 'subgroup_tex': 'C_{80}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.5', 'subgroup_hash': 5, 'subgroup_order': 160, 'subgroup_tex': 'C_{80}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.70', 'subgroup_hash': 70, 'subgroup_order': 160, 'subgroup_tex': 'C_{40}.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.5', 'subgroup_hash': 5, 'subgroup_order': 160, 'subgroup_tex': 'C_{80}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.324.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.5', 'subgroup_hash': 5, 'subgroup_order': 160, 'subgroup_tex': 'C_{80}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 223462118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.g1.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': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 223462119
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.120', 'subgroup_hash': 120, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 223462122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.120', 'subgroup_hash': 120, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 223462123
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.116', 'subgroup_hash': 116, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
  • id: 223462126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.120', 'subgroup_hash': 120, 'subgroup_order': 144, 'subgroup_tex': 'C_2.\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 223462127
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.360.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.185', 'subgroup_hash': 185, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '51840.cr.405.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '405.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': 405, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.886', 'subgroup_hash': 886, 'subgroup_order': 128, 'subgroup_tex': '\\OD_{32}:C_4', 'supersolvable': True, 'sylow': 2}
  • id: 223462130
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 223462139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 223462140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.480.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462142
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 219, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '51840.cr.640.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '640.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '640.6185', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6185, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 640, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{40}:C_4.C_2', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 3}
  • id: 223462144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.36', 'subgroup_hash': 36, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462146
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.23', 'subgroup_hash': 23, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 223462147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.9', 'subgroup_hash': 9, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.32', 'subgroup_hash': 32, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.4', 'subgroup_hash': 4, 'subgroup_order': 80, 'subgroup_tex': 'C_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.4', 'subgroup_hash': 4, 'subgroup_order': 80, 'subgroup_tex': 'C_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.29', 'subgroup_hash': 29, 'subgroup_order': 80, 'subgroup_tex': 'C_5:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.29', 'subgroup_hash': 29, 'subgroup_order': 80, 'subgroup_tex': 'C_5:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.4', 'subgroup_hash': 4, 'subgroup_order': 80, 'subgroup_tex': 'C_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.4', 'subgroup_hash': 4, 'subgroup_order': 80, 'subgroup_tex': 'C_8\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.29', 'subgroup_hash': 29, 'subgroup_order': 80, 'subgroup_tex': 'C_5:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462160
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.648.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.2', 'subgroup_hash': 2, 'subgroup_order': 80, 'subgroup_tex': 'C_{80}', 'supersolvable': True, 'sylow': 0}
  • id: 223462161
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.648.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.n1.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.2', 'subgroup_hash': 2, 'subgroup_order': 80, 'subgroup_tex': 'C_{80}', 'supersolvable': True, 'sylow': 0}
  • id: 223462162
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.1', 'subgroup_hash': 1, 'subgroup_order': 80, 'subgroup_tex': 'C_5:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462163
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.648.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '648.o1.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.1', 'subgroup_hash': 1, 'subgroup_order': 80, 'subgroup_tex': 'C_5:C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.d2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.d2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 223462171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.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': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462177
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462178
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462179
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462180
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462181
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462182
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462183
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.q1.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': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
  • id: 223462188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462189
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.720.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.106', 'subgroup_hash': 106, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.110', 'subgroup_hash': 110, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.184', 'subgroup_hash': 184, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times \\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 223462193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.46', 'subgroup_hash': 46, 'subgroup_order': 64, 'subgroup_tex': 'C_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.46', 'subgroup_hash': 46, 'subgroup_order': 64, 'subgroup_tex': 'C_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.d1.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.46', 'subgroup_hash': 46, 'subgroup_order': 64, 'subgroup_tex': 'C_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.810.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '810.d1.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': 810, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.46', 'subgroup_hash': 46, 'subgroup_order': 64, 'subgroup_tex': 'C_{16}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462197
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.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': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462200
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.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': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.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': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.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': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.960.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1080.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1080.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': 1080, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462207
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 223462208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462211
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.g1.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462216
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462217
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 223462218
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1296.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
  • id: 223462219
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462221
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462222
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.3', 'subgroup_hash': 3, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462223
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.n1.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': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.3', 'subgroup_hash': 3, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462224
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1296.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1296.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1296, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.a2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.a2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462227
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.a3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.a3.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.c2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462233
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.k2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462244
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.l2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.l2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462245
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.n2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.n2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 223462250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.p1.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 223462251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1440.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.q1.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': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 223462253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462258
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.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': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.13', 'subgroup_hash': 13, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 223462266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 223462267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.15', 'subgroup_hash': 15, 'subgroup_order': 32, 'subgroup_tex': 'C_8.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 223462269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1620.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1620.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1620, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.17', 'subgroup_hash': 17, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{32}', 'supersolvable': True, 'sylow': 0}
  • id: 223462270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.1920.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1920.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': 1920, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 223462271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 223462272
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 223462273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 223462275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 223462277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.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': 2160, 'quotient_simple': 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: 223462278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2160.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2160.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2160, 'quotient_simple': 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: 223462279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.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': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.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': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.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': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.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': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462283
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.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': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 223462284
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2592.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': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 223462285
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462286
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462288
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462289
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462290
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2592.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2592.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2592, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.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': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.a2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.a2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462293
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.a3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.a3.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.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': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.b3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.b3.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.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': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.c2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.c3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.c3.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.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': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462302
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.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': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.e2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.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': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.h2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462308
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.2880.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2880.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462310
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462311
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462312
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 2, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462314
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462318
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 223462323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462326
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462327
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.n1.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462328
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462329
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.3240.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3240.o1.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': 3240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 223462330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.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': 4320, 'quotient_simple': 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: 223462332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.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': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 223462333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.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': 4320, 'quotient_simple': 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: 223462334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.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': 4320, 'quotient_simple': 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: 223462335
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.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': 4320, 'quotient_simple': 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: 223462336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.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': 4320, 'quotient_simple': 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: 223462337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': 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: 223462338
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 223462339
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4320.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 223462340
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': 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: 223462341
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.4320.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4320.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4320, 'quotient_simple': 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: 223462344
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 400, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.5184.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.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': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462345
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.5184.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.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': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462346
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.5184.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5184.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': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 223462347
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.5184.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.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': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462348
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.5184.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5184.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': 5184, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 223462349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.5760.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5760.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': 5760, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.5760.a2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5760.a2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5760, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.5760.a3.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5760.a3.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5760, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 223462352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.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': 6480, 'quotient_simple': 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: 223462353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 2, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.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': 6480, 'quotient_simple': 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: 223462355
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.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': 6480, 'quotient_simple': 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: 223462356
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.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': 6480, 'quotient_simple': 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: 223462357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.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': 6480, 'quotient_simple': 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: 223462358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.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': 6480, 'quotient_simple': 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: 223462359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 223462360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.g1.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': 6480, 'quotient_simple': 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: 223462361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 223462362
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 223462363
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462364
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462366
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462367
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462368
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462369
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.n1.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': 6480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 223462370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.6480.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6480.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6480, 'quotient_simple': 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: 223462371
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 2, 'counter': 425, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.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': 8640, 'quotient_simple': 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: 223462372
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8640.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': 8640, 'quotient_simple': 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: 223462373
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8640.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': 8640, 'quotient_simple': 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: 223462374
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.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': 8640, 'quotient_simple': 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: 223462375
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8640.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': 8640, 'quotient_simple': 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: 223462377
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8640.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': 8640, 'quotient_simple': 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: 223462378
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.8640.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8640.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8640, 'quotient_simple': 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: 223462379
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '51840.cr.10368.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10368.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': 10368, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 223462380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 640, 'characteristic': False, 'core_order': 2, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.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': 12960, 'quotient_simple': 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: 223462381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 2, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.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': 12960, 'quotient_simple': 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: 223462382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.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': 12960, 'quotient_simple': 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: 223462383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.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': 12960, 'quotient_simple': 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: 223462384
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.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': 12960, 'quotient_simple': 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: 223462385
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.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': 12960, 'quotient_simple': 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: 223462386
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 223462388
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 440, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 223462389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 223462390
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 442, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 223462391
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.12960.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12960.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12960, 'quotient_simple': 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: 223462392
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.17280.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '17280.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': 17280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 223462393
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 51840, 'characteristic': True, 'core_order': 2, 'counter': 445, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '51840.cr.25920.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '25920.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '25920.dn', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1549518908401167474, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 25920, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_{81}:C_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 223462394
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 640, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.25920.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.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': 25920, '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: 223462395
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 640, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.25920.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.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': 25920, '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: 223462396
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.25920.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.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': 25920, '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: 223462397
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 449, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '51840.cr.25920.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25920.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': 25920, '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: 223462399
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '51840.cr', 'ambient_counter': 70, 'ambient_order': 51840, 'ambient_tex': 'C_2\\times F_{81}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 51840, 'characteristic': True, 'core_order': 1, 'counter': 450, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '51840.cr.51840.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '51840.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '51840.cr', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8363559991699411848, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 51840, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times F_{81}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D3', 'C9'], '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: 223462009
    {'ambient': '51840.cr', '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': '25920.a1.a1', 'complements': ['51840.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1', '5.a1.a1', '81.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1468, 5127, 8266, 5319, 8555, 5072, 8426, 4654], 'generators': [8000, 1, 20, 17280, 160, 2, 64, 41280, 80, 8640, 40, 23040], 'label': '51840.cr.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '25920.dn', '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': '25920.dn'}
  • id: 223462010
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['12960.j1.a1', '12960.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.h1.b1', '20.a1.a1', '324.d1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1063, 9299, 8785, 9619, 9246, 1053, 9763, 358], 'generators': [40320, 960, 8640, 160, 40, 46400, 20, 64, 80, 17280], 'label': '51840.cr.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.b1.a1', '8.h1.b1', '8.h1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462011
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '20.d1.a1'], 'contains': ['80.e1.a1', '80.n1.a1', '80.n1.b1', '360.f1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2353, -1, 6276, -1, 6102, -1, 5691, -1], 'generators': [21, 8000, 6720, 8640, 160, 17280, 5760, 82], 'label': '51840.cr.40.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.f1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3508'}
  • id: 223462012
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '20.b1.a1', '20.f1.a1', '20.g1.a1'], 'contains': ['80.g1.a1', '80.i1.a1', '360.g1.a1', '360.h1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4225, -1, 5174, -1, 4928, -1, 5184, -1], 'generators': [1, 1280, 6720, 80, 160, 17280, 40320, 2], 'label': '51840.cr.40.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.lt'}
  • id: 223462013
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '20.b1.a1', '20.f1.b1', '20.g1.a1'], 'contains': ['80.g1.a1', '80.i1.b1', '360.g1.b1', '360.h1.b1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4225, -1, 5303, -1, 4928, -1, 5288, -1], 'generators': [8641, 1280, 6720, 80, 160, 17280, 40320, 2], 'label': '51840.cr.40.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.g1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2592.lt'}
  • id: 223462014
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.c1.a1', '20.f1.a1', '20.f1.b1', '20.h1.a1', '20.h1.b1', '20.i1.a1', '20.i1.b1'], 'contains': ['80.b1.a1', '80.g1.a1', '80.m1.a1', '360.i1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2887, -1, 7722, -1, 7844, -1, 7662, -1], 'generators': [2, 8000, 6720, 40, 160, 17280, 5760, 80], 'label': '51840.cr.40.h1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462015
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '20.c1.a1', '20.g1.a1', '20.j1.a1'], 'contains': ['80.c1.a1', '80.g1.a1', '80.l1.a1', '360.j1.a1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3775, -1, 5700, -1, 6547, -1, 6478, -1], 'generators': [8680, 8000, 6720, 2, 160, 17280, 5760, 80], 'label': '51840.cr.40.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462016
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '20.d1.a1', '20.h1.a1', '20.j1.a1'], 'contains': ['80.g1.a1', '80.n1.a1', '3240.i1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2520, -1, 6602, -1, 7368, -1, 6107, -1], 'generators': [21, 34880, 47040, 80, 160, 17280, 5760, 82], 'label': '51840.cr.40.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.ct'}
  • id: 223462017
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '20.d1.a1', '20.h1.b1', '20.j1.a1'], 'contains': ['80.g1.a1', '80.n1.b1', '3240.i1.b1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2520, -1, 6743, -1, 7368, -1, 6251, -1], 'generators': [8661, 34880, 47040, 80, 160, 17280, 5760, 82], 'label': '51840.cr.40.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.j1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2592.ct'}
  • id: 223462018
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '20.b1.a1'], 'contains': ['80.h1.a1', '80.i1.a1', '80.i1.b1', '360.k1.a1', '360.l1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [5709, -1, 3804, -1, 4057, -1, 3940, -1], 'generators': [1, 11840, 6720, 8720, 160, 17280, 40320, 2], 'label': '51840.cr.40.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3499'}
  • id: 223462019
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '20.c1.a1', '20.k1.a1', '20.k1.b1'], 'contains': ['80.b1.a1', '80.j1.a1', '80.l1.a1', '360.m1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3470, -1, 7421, -1, 7683, -1, 7941, -1], 'generators': [8642, 8000, 6720, 40, 160, 17280, 5760, 80], 'label': '51840.cr.40.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.l1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462020
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '20.c1.a1'], 'contains': ['80.c1.a1', '80.j1.a1', '80.m1.a1', '360.n1.a1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3618, -1, 5963, -1, 6664, -1, 6375, -1], 'generators': [8680, 8000, 6720, 42, 160, 17280, 5760, 80], 'label': '51840.cr.40.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.m1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462021
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['12960.j1.a1', '12960.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.b1.a1', '8.i1.a1', '8.i1.b1', '20.e1.a1', '324.e1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [538, 8262, 9232, 7561, 8697, 3387, 8907, 1817], 'generators': [23040, 960, 8640, 64, 80, 12800, 182, 200, 160, 17280], 'label': '51840.cr.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.a1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462022
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '20.d1.a1'], 'contains': ['80.k1.a1', '80.n1.a1', '80.n1.b1', '3240.m1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2185, -1, 6138, -1, 6408, -1, 5831, -1], 'generators': [21, 34880, 47040, 8720, 160, 17280, 5760, 82], 'label': '51840.cr.40.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3508'}
  • id: 223462023
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '20.e1.a1', '20.i1.b1', '20.k1.a1'], 'contains': ['80.b1.a1', '3240.o1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [939, -1, 8806, -1, 8781, -1, 8683, -1], 'generators': [8822, 25280, 29760, 200, 160, 17280, 40320, 80], 'label': '51840.cr.40.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.o1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462024
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '20.e1.a1', '20.i1.a1', '20.k1.b1'], 'contains': ['80.b1.a1', '3240.o1.b1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [939, -1, 9004, -1, 8781, -1, 8582, -1], 'generators': [182, 25280, 29760, 200, 160, 17280, 40320, 80], 'label': '51840.cr.40.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.o1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.o1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462025
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['810.d1.a1', '810.d1.d1', '810.d1.b1', '810.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.h1.a1'], 'contains': ['128.a1.a1', '320.a1.a1', '5184.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6312, 2232, 1841, 1836, 3545, 7631, 134, 7841], 'generators': [8640, 17280, 29120, 47040, 64, 23040], 'label': '51840.cr.64.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1', '320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': '64.46', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462026
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'contains': ['128.a1.a1', '320.b1.a1', '5184.b1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5905, 3208, 2460, 2933, 3984, 6960, 2135, 7244], 'generators': [160, 17280, 8000, 12480, 64, 40320], 'label': '51840.cr.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.f1.a1', '32.g1.a1'], 'normal_contains': ['128.a1.a1', '320.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462027
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['810.d1.a1', '810.d1.d1', '810.d1.b1', '810.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.i1.a1'], 'contains': ['128.a1.a1', '320.c1.a1', '5184.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6552, 1527, 1147, 2428, 3412, 8301, 546, 8437], 'generators': [8800, 17280, 8000, 12480, 64, 40320], 'label': '51840.cr.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1', '320.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '64.46', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462028
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.h1.a1', '32.i1.a1', '32.j1.a1', '32.j1.b1'], 'contains': ['128.a1.a1', '320.d1.a1', '5184.d1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6824, -1, 1057, -1, 3185, -1, 454, -1], 'generators': [2, 17280, 11840, 41280, 64, 5760], 'label': '51840.cr.64.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462029
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.h1.a1', '32.i1.a1'], 'contains': ['128.a1.a1', '320.e1.a1', '5184.e1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6727, -1, 954, -1, 3277, -1, 315, -1], 'generators': [8642, 17280, 11840, 41280, 64, 5760], 'label': '51840.cr.64.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462030
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '40.a1.a1', '40.c1.a1', '40.e1.a1'], 'contains': ['160.a1.a1', '160.b1.a1', '160.c1.a1', '720.c1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5337, 5522, 4427, 4374, 5058, 4168, 4855, 4785], 'generators': [8640, 5760, 6720, 80, 17280, 160, 11840], 'label': '51840.cr.80.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.b1.a1', '40.a1.a1'], 'normal_contains': ['160.a1.a1', '160.b1.a1', '160.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462031
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '40.a1.a1', '40.b1.a1', '40.b1.b1', '40.h1.a1', '40.l1.a1', '40.o1.a1', '40.o1.b1'], 'contains': ['160.b1.a1', '720.m1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2639, 8034, 8034, 7118, 7572, 2181, 7858, 2748], 'generators': [40, 5760, 6720, 80, 17280, 160, 8000], 'label': '51840.cr.80.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.b1.a1', 'normal_contained_in': ['16.h1.a1', '40.a1.a1', '40.b1.b1', '40.b1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462032
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'contains': ['8.d1.a1', '8.l1.a1', '20.f1.a1', '324.f1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2899, 3699, 7547, 5027, 7459, 5530, 7321, 4993], 'generators': [23040, 41280, 40, 64, 80, 8000, 1, 2, 160, 17280], 'label': '51840.cr.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.d1.b1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462033
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '40.a1.a1', '40.i1.a1', '40.m1.a1'], 'contains': ['160.b1.a1', '720.n1.a1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3469, 7268, 5932, 6091, 6578, 3089, 6324, 3854], 'generators': [8680, 5760, 6720, 80, 17280, 160, 8000], 'label': '51840.cr.80.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1.a1', 'normal_contained_in': ['16.i1.a1', '40.a1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462034
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.c1.a1', '40.d1.a1'], 'contains': ['160.a1.a1', '160.d1.a1', '160.e1.a1', '160.f1.a1', '160.i1.a1', '240.a1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7883, -1, 1673, -1, 1744, -1, 1897, -1], 'generators': [8640, 5760, 6720, 2, 17280, 160, 8000], 'label': '51840.cr.80.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462035
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '40.c1.a1', '40.f1.a1'], 'contains': ['160.a1.a1', '160.g1.a1', '160.h1.a1', '720.d1.a1', '720.d2.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4469, -1, 4778, -1, 4378, -1, 4501, -1], 'generators': [8640, 5760, 6720, 82, 17280, 160, 8000], 'label': '51840.cr.80.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462036
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '40.d1.a1'], 'contains': ['160.d1.a1', '160.j1.a1', '160.j1.b1', '240.b1.a1', '240.c1.a1', '720.e1.a1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7009, -1, 2437, -1, 2401, -1, 2642, -1], 'generators': [1, 6720, 1280, 8640, 40320, 17280, 2], 'label': '51840.cr.80.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.f1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462037
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '40.c1.a1', '40.g1.a1', '40.g1.b1', '40.h1.a1', '40.i1.a1', '40.j1.a1', '40.j1.b1'], 'contains': ['160.b1.a1', '160.e1.a1', '160.g1.a1', '720.g1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4667, -1, 5262, -1, 5276, -1, 5274, -1], 'generators': [2, 5760, 6720, 80, 17280, 160, 8000], 'label': '51840.cr.80.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462038
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '40.c1.a1', '40.k1.a1'], 'contains': ['160.c1.a1', '160.e1.a1', '160.h1.a1', '720.h1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5863, -1, 3929, -1, 3683, -1, 4053, -1], 'generators': [8720, 5760, 6720, 2, 17280, 160, 11840], 'label': '51840.cr.80.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462039
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '40.d1.a1', '40.g1.a1', '40.k1.a1'], 'contains': ['160.e1.a1', '160.j1.a1', '240.d1.a1', '720.i1.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7225, -1, 2260, -1, 3047, -1, 2987, -1], 'generators': [1, 40320, 6720, 160, 17280, 2, 1280], 'label': '51840.cr.80.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '80.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3499'}
  • id: 223462040
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '40.d1.a1', '40.g1.b1', '40.k1.a1'], 'contains': ['160.e1.a1', '160.j1.b1', '240.d1.b1', '720.i1.b1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7225, -1, 3033, -1, 3047, -1, 3668, -1], 'generators': [8641, 40320, 6720, 160, 17280, 2, 1280], 'label': '51840.cr.80.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '80.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3499'}
  • id: 223462041
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '40.c1.a1', '40.l1.a1', '40.m1.a1'], 'contains': ['160.b1.a1', '160.f1.a1', '160.h1.a1', '720.k1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5139, -1, 4616, -1, 4871, -1, 5021, -1], 'generators': [8642, 5760, 6720, 80, 17280, 160, 8000], 'label': '51840.cr.80.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.j1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462042
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '40.c1.a1', '40.n1.a1'], 'contains': ['160.c1.a1', '160.f1.a1', '160.g1.a1', '720.l1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4936, -1, 4238, -1, 4679, -1, 4335, -1], 'generators': [8720, 5760, 6720, 82, 17280, 160, 11840], 'label': '51840.cr.80.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.k1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462043
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'contains': ['8.d1.a1', '8.l1.b1', '20.f1.b1', '324.f1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2899, 3699, 7765, 4407, 7459, 5530, 7473, 6178], 'generators': [23040, 41280, 40, 64, 80, 8000, 8641, 2, 160, 17280], 'label': '51840.cr.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.c1', '2.d1.d1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462044
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '40.e1.a1', '40.i1.a1', '40.l1.a1'], 'contains': ['160.b1.a1', '720.o1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3873, -1, 5770, -1, 6670, -1, 6582, -1], 'generators': [8682, 5760, 6720, 80, 17280, 160, 8000], 'label': '51840.cr.80.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.l1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462045
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '40.e1.a1', '40.h1.a1', '40.m1.a1'], 'contains': ['160.b1.a1', '720.p1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3710, -1, 6067, -1, 6762, -1, 6406, -1], 'generators': [42, 5760, 6720, 80, 17280, 160, 8000], 'label': '51840.cr.80.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '80.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.m1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462046
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '40.f1.a1', '40.j1.a1', '40.n1.a1'], 'contains': ['160.g1.a1', '720.q1.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2261, -1, 6148, -1, 6486, -1, 6077, -1], 'generators': [21, 5760, 6720, 82, 17280, 160, 8000], 'label': '51840.cr.80.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '80.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3508'}
  • id: 223462047
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '40.f1.a1', '40.j1.b1', '40.n1.a1'], 'contains': ['160.g1.a1', '720.q1.b1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2261, -1, 6283, -1, 6486, -1, 6187, -1], 'generators': [8661, 5760, 6720, 82, 17280, 160, 8000], 'label': '51840.cr.80.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '80.n1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3508'}
  • id: 223462048
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '80.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '40.d1.a1'], 'contains': ['160.i1.a1', '160.j1.a1', '160.j1.b1', '240.e1.a1', '240.e1.b1', '720.r1.a1'], 'core': '320.c1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7610, -1, 2705, -1, 2131, -1, 2363, -1], 'generators': [1, 40320, 6720, 8800, 17280, 2, 1280], 'label': '51840.cr.80.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.o1.a1', 'subgroup_fusion': None, 'weyl_group': '648.716'}
  • id: 223462049
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.c1.a1', '162.d1.a1', '162.d1.b1', '162.d1.c1', '162.d1.d1', '405.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [850, -1, 8795, -1, 9712, -1, 9072, -1], 'generators': [1, 40, 160, 8640, 80, 64, 20, 2], 'label': '51840.cr.81.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462050
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['180.a1.a1', '180.b1.a1', '180.c1.a1', '180.d1.a1', '180.d1.b1', '180.e1.a1', '180.e1.b1', '810.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3783, -1, 6251, -1, 5927, -1, 7118, -1], 'generators': [1, 80, 160, 8640, 2, 6720, 1280, 40], 'label': '51840.cr.90.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462051
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.c1.a1', '240.d1.a1', '240.d1.b1', '240.e1.a1', '240.e1.b1', '360.c1.a1', '1080.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [6938, -1, 2538, -1, 2636, -1, 3157, -1], 'generators': [1, 6720, 1280, 8640, 17280, 160, 2], 'label': '51840.cr.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462052
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['405.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1'], 'contains': ['640.a1.a1', '10368.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6445, 1897, 986, 2489, 3541, 7631, 36, 7841], 'generators': [64, 47040, 23040, 29120, 17280], 'label': '51840.cr.128.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'normal_contains': ['640.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '64.46', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462053
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '80.a1.a1', '80.d1.a1', '80.e1.a1'], 'contains': ['320.a1.a1', '320.b1.a1', '320.c1.a1', '480.a1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7276, 2809, 2042, 2071, 1892, 6204, 1641, 6571], 'generators': [8640, 17280, 5760, 160, 8000, 6720], 'label': '51840.cr.160.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': ['32.a1.a1', '80.a1.a1'], 'normal_contains': ['320.a1.a1', '320.b1.a1', '320.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462054
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'contains': ['8.d1.a1', '8.m1.a1', '20.h1.a1', '324.h1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2190, 4662, 7907, 3819, 8395, 6409, 7789, 4400], 'generators': [23040, 12480, 40, 64, 80, 2240, 21, 82, 160, 17280], 'label': '51840.cr.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.d1.c1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462055
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '80.a1.a1', '80.b1.a1', '80.c1.a1', '80.g1.a1', '80.j1.a1', '80.l1.a1', '80.m1.a1'], 'contains': ['320.b1.a1', '1440.i1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4830, 5522, 4694, 4911, 5147, 4168, 4906, 4785], 'generators': [80, 17280, 5760, 160, 11840, 6720], 'label': '51840.cr.160.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '160.b1.a1', 'normal_contained_in': ['32.d1.a1', '80.a1.a1', '80.c1.a1', '80.b1.a1'], 'normal_contains': ['320.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462056
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '80.a1.a1', '80.h1.a1', '80.k1.a1'], 'contains': ['320.b1.a1', '1440.j1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5922, 3862, 3893, 3837, 4116, 5358, 3944, 5818], 'generators': [8720, 17280, 5760, 160, 11840, 6720], 'label': '51840.cr.160.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '160.c1.a1', 'normal_contained_in': ['32.e1.a1', '80.a1.a1'], 'normal_contains': ['320.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462057
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '80.d1.a1', '80.f1.a1'], 'contains': ['320.a1.a1', '320.d1.a1', '320.e1.a1', '480.b1.a1', '480.c1.a1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7546, -1, 1585, -1, 1080, -1, 684, -1], 'generators': [8640, 6720, 8000, 2, 5760, 17280], 'label': '51840.cr.160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '160.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '288.843'}
  • id: 223462058
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '80.d1.a1', '80.g1.a1', '80.h1.a1', '80.i1.a1', '80.i1.b1'], 'contains': ['320.b1.a1', '320.d1.a1', '480.d1.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7972, -1, 1750, -1, 1744, -1, 2036, -1], 'generators': [2, 17280, 5760, 160, 8000, 6720], 'label': '51840.cr.160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '160.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462059
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '80.d1.a1', '80.j1.a1', '80.k1.a1'], 'contains': ['320.b1.a1', '320.e1.a1', '480.e1.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8528, -1, 1425, -1, 1252, -1, 1773, -1], 'generators': [8642, 17280, 5760, 160, 8000, 6720], 'label': '51840.cr.160.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '160.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.f1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462060
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '80.e1.a1', '80.g1.a1', '80.k1.a1', '80.n1.a1', '80.n1.b1'], 'contains': ['320.b1.a1', '1440.k1.a1', '1440.k2.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4493, -1, 4824, -1, 4904, -1, 4636, -1], 'generators': [82, 17280, 5760, 160, 8000, 6720], 'label': '51840.cr.160.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '160.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.g1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462061
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '80.e1.a1', '80.h1.a1', '80.j1.a1'], 'contains': ['320.b1.a1', '1440.l1.a1', '1440.l2.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5463, -1, 4346, -1, 3852, -1, 4365, -1], 'generators': [8722, 17280, 5760, 160, 8000, 6720], 'label': '51840.cr.160.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '160.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.h1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462062
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '80.d1.a1', '80.o1.a1'], 'contains': ['320.c1.a1', '320.d1.a1', '320.e1.a1', '480.f1.a1', '480.g1.a1'], 'core': '320.c1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8413, -1, 804, -1, 695, -1, 877, -1], 'generators': [8800, 17280, 5760, 2, 8000, 6720], 'label': '51840.cr.160.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '160.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.lt'}
  • id: 223462063
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '80.f1.a1', '80.i1.a1', '80.o1.a1'], 'contains': ['320.d1.a1', '480.h1.a1', '480.i1.a1', '1440.p1.a1'], 'core': '640.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7816, -1, 1879, -1, 1596, -1, 1905, -1], 'generators': [1, 40320, 6720, 17280, 2, 1280], 'label': '51840.cr.160.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '160.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.j1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462064
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '160.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.b1', '80.f1.a1', '80.i1.b1', '80.o1.a1'], 'contains': ['320.d1.a1', '480.h1.b1', '480.i1.b1', '1440.p1.b1'], 'core': '640.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7816, -1, 2850, -1, 1596, -1, 2553, -1], 'generators': [8641, 40320, 6720, 17280, 2, 1280], 'label': '51840.cr.160.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '160.j1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.j1.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462065
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'contains': ['8.d1.a1', '8.m1.b1', '20.h1.b1', '324.h1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2190, 4662, 8016, 5614, 8395, 6409, 8120, 5586], 'generators': [23040, 12480, 40, 64, 80, 2240, 8661, 82, 160, 17280], 'label': '51840.cr.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.d1.d1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462066
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.b1.a1', '324.f1.a1', '324.f1.b1', '324.g1.a1', '810.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2117, -1, 7921, -1, 8428, -1, 7970, -1], 'generators': [1, 160, 40, 2, 8640, 64, 80], 'label': '51840.cr.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462067
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.c1.a1', '324.h1.a1', '324.h1.b1', '324.j1.a1', '810.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1167, -1, 8260, -1, 9020, -1, 8344, -1], 'generators': [21, 160, 40, 82, 8640, 64, 80], 'label': '51840.cr.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462068
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.d1.a1', '324.e1.a1', '324.i1.a1', '324.i1.b1', '324.k1.a1', '324.k1.b1', '810.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [411, -1, 9400, -1, 9731, -1, 9553, -1], 'generators': [20, 160, 2, 40, 8640, 64, 80], 'label': '51840.cr.162.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462069
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '81.a1.a1'], 'contains': ['324.f1.a1', '324.h1.a1', '324.i1.a1', '810.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [779, -1, 8636, -1, 9282, -1, 8607, -1], 'generators': [1, 160, 2, 40, 20, 64, 80], 'label': '51840.cr.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.a1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462070
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '81.a1.a1'], 'contains': ['324.f1.a1', '324.h1.b1', '324.i1.b1', '810.d1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [779, -1, 8901, -1, 9282, -1, 9154, -1], 'generators': [1, 160, 2, 40, 8660, 64, 80], 'label': '51840.cr.162.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.b1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462071
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '81.a1.a1'], 'contains': ['324.f1.b1', '324.h1.a1', '324.i1.b1', '810.d1.c1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [779, -1, 8742, -1, 9282, -1, 8822, -1], 'generators': [8641, 160, 2, 40, 8660, 64, 80], 'label': '51840.cr.162.d1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.c1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.c1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462072
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '81.a1.a1'], 'contains': ['324.f1.b1', '324.h1.b1', '324.i1.a1', '810.d1.d1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [779, -1, 8530, -1, 9282, -1, 8715, -1], 'generators': [8641, 160, 2, 40, 20, 64, 80], 'label': '51840.cr.162.d1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.d1.d1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.d1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462073
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '90.a1.a1'], 'contains': ['360.a1.a1', '360.b1.a1', '360.g1.a1', '360.g1.b1', '360.k1.a1', '1620.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5050, -1, 4928, -1, 5667, -1, 5540, -1], 'generators': [1, 17600, 160, 8640, 18240, 80, 2], 'label': '51840.cr.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462074
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '90.a1.a1'], 'contains': ['360.a1.a1', '360.c1.a1', '360.h1.a1', '360.h1.b1', '360.l1.a1', '1620.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4732, -1, 5109, -1, 5459, -1, 5725, -1], 'generators': [1, 1280, 160, 8640, 6720, 80, 2], 'label': '51840.cr.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462075
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '90.a1.a1'], 'contains': ['360.a1.a1', '360.d1.a1', '360.e1.a1', '360.i1.a1', '360.j1.a1', '360.m1.a1', '360.n1.a1', '1620.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3129, -1, 7055, -1, 7194, -1, 6960, -1], 'generators': [8640, 11840, 160, 2, 6720, 40, 80], 'label': '51840.cr.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462076
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'contains': ['8.d1.a1', '8.h1.a1', '8.i1.b1', '20.i1.a1', '324.i1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [717, 6636, 8923, 6198, 9089, 2537, 8757, 3192], 'generators': [5760, 24000, 2, 64, 80, 34880, 20, 40, 160, 17280], 'label': '51840.cr.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.d1.d1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '51840.cr', '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': '25920.dn'}
  • id: 223462077
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.a1', '90.a1.a1'], 'contains': ['360.g1.a1', '360.h1.a1', '360.i1.a1', '1620.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3783, -1, 6593, -1, 6371, -1, 6804, -1], 'generators': [1, 1280, 160, 40, 6720, 2, 80], 'label': '51840.cr.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462078
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.b1', '90.a1.a1'], 'contains': ['360.g1.b1', '360.h1.b1', '360.i1.a1', '1620.f1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3783, -1, 6357, -1, 6371, -1, 6870, -1], 'generators': [8641, 1280, 160, 40, 6720, 2, 80], 'label': '51840.cr.180.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.b1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462079
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.g1.a1', '90.a1.a1'], 'contains': ['360.g1.a1', '360.h1.b1', '360.j1.a1', '1620.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3704, -1, 5985, -1, 6297, -1, 6655, -1], 'generators': [1, 2240, 160, 8680, 18240, 2, 80], 'label': '51840.cr.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462080
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.g1.a1', '90.a1.a1'], 'contains': ['360.g1.b1', '360.h1.a1', '360.j1.a1', '1620.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3704, -1, 5613, -1, 6297, -1, 6480, -1], 'generators': [1, 1280, 160, 8680, 6720, 2, 80], 'label': '51840.cr.180.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '180.e1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.b1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462081
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.d1.a1', '120.a1.a1'], 'contains': ['480.a1.a1', '480.b1.a1', '480.c1.a1', '480.d1.a1', '480.e1.a1', '480.f1.a1', '480.g1.a1', '720.a1.a1', '720.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8162, -1, 1322, -1, 1404, -1, 1316, -1], 'generators': [8640, 17280, 6720, 2, 160, 8000], 'label': '51840.cr.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462082
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '120.a1.a1'], 'contains': ['480.c1.a1', '480.h1.a1', '480.h1.b1', '720.f1.a1', '2160.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [6940, -1, 2266, -1, 2413, -1, 2872, -1], 'generators': [1, 6720, 1280, 8640, 17280, 2], 'label': '51840.cr.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 223462083
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '120.a1.a1'], 'contains': ['480.c1.a1', '480.i1.a1', '480.i1.b1', '720.f1.a1', '2160.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [6757, -1, 2114, -1, 2239, -1, 2718, -1], 'generators': [1, 40320, 6720, 8640, 2, 1280], 'label': '51840.cr.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '240.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462084
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.i1.a1', '120.a1.a1'], 'contains': ['480.d1.a1', '480.h1.a1', '480.i1.a1', '720.j1.a1', '2160.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7405, -1, 1964, -1, 2636, -1, 3015, -1], 'generators': [1, 17280, 6720, 160, 2, 1280], 'label': '51840.cr.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462085
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.i1.b1', '120.a1.a1'], 'contains': ['480.d1.a1', '480.h1.b1', '480.i1.b1', '720.j1.b1', '2160.d1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7405, -1, 2790, -1, 2636, -1, 3157, -1], 'generators': [8641, 17280, 6720, 160, 2, 1280], 'label': '51840.cr.240.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462086
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.o1.a1', '120.a1.a1'], 'contains': ['480.g1.a1', '480.h1.a1', '480.i1.b1', '720.s1.a1', '2160.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7874, -1, 2544, -1, 2066, -1, 2257, -1], 'generators': [1, 17280, 6720, 8800, 2, 1280], 'label': '51840.cr.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462087
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'contains': ['8.d1.a1', '8.h1.b1', '8.i1.a1', '20.i1.b1', '324.i1.b1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [717, 6636, 9073, 6811, 9089, 2537, 9256, 3811], 'generators': [5760, 24000, 2, 64, 80, 34880, 8660, 40, 160, 17280], 'label': '51840.cr.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.d1.c1'], 'normal_contains': ['8.d1.a1', '8.h1.b1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '51840.cr', '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': '25920.dn'}
  • id: 223462088
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.o1.a1', '120.a1.a1'], 'contains': ['480.g1.a1', '480.h1.b1', '480.i1.a1', '720.s1.a1', '2160.e1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7874, -1, 2405, -1, 2066, -1, 2399, -1], 'generators': [1, 40320, 6720, 8800, 2, 1280], 'label': '51840.cr.240.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '240.e1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462089
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': ['162.d1.a1', '162.d1.d1', '162.d1.b1', '162.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '160.a1.a1', '160.d1.a1'], 'contains': ['640.a1.a1', '960.a1.a1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7539, 2809, 1517, 1577, 1063, 6445, 134, 6786], 'generators': [8640, 17280, 8000, 6720, 5760], 'label': '51840.cr.320.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': ['64.a1.a1', '160.a1.a1'], 'normal_contains': ['640.a1.a1', '25920.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '320.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': '320.186', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '320.186'}
  • id: 223462090
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1', '160.e1.a1', '160.f1.a1', '160.g1.a1', '160.h1.a1'], 'contains': ['640.a1.a1', '960.b1.a1'], 'core': '320.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7189, 3479, 1708, 2933, 2059, 5807, 1956, 6219], 'generators': [160, 17280, 8000, 6720, 5760], 'label': '51840.cr.320.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': ['64.b1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1'], 'normal_contains': ['640.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '320.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462091
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['162.d1.a1', '162.d1.d1', '162.d1.b1', '162.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '160.a1.a1', '160.i1.a1'], 'contains': ['640.a1.a1', '960.c1.a1'], 'core': '320.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8518, 2137, 975, 2139, 630, 7083, 409, 7353], 'generators': [8800, 17280, 8000, 6720, 5760], 'label': '51840.cr.320.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': ['64.c1.a1', '160.a1.a1'], 'normal_contains': ['640.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '320.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '320.186', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '320.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462092
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '320.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '160.d1.a1', '160.e1.a1', '160.i1.a1', '160.j1.a1', '160.j1.b1'], 'contains': ['640.a1.a1', '960.d1.a1', '960.e1.a1'], 'core': '640.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8730, -1, 722, -1, 490, -1, 684, -1], 'generators': [2, 6720, 5760, 17280, 8000], 'label': '51840.cr.320.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '320.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.d1.a1', 'subgroup_fusion': None, 'weyl_group': '288.843'}
  • id: 223462093
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '320.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '160.d1.a1', '160.f1.a1', '160.i1.a1'], 'contains': ['640.a1.a1', '960.f1.a1', '960.g1.a1'], 'core': '640.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8923, -1, 481, -1, 69, -1, 258, -1], 'generators': [8642, 6720, 5760, 17280, 8000], 'label': '51840.cr.320.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '320.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.e1.a1', 'subgroup_fusion': None, 'weyl_group': '288.843'}
  • id: 223462094
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '162.a1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.f1.a1', '648.f1.b1', '648.j1.a1', '1620.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [4354, -1, 5694, -1, 6876, -1, 5905, -1], 'generators': [1, 64, 80, 2, 8640, 160], 'label': '51840.cr.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462095
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '162.a1.a1', '162.b1.a1', '162.c1.a1'], 'contains': ['648.a1.a1', '648.c1.a1', '648.d1.a1', '648.g1.a1', '648.h1.a1', '648.k1.a1', '648.l1.a1', '1620.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1928, -1, 8107, -1, 8670, -1, 8167, -1], 'generators': [8640, 64, 40, 80, 2, 160], 'label': '51840.cr.324.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462096
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '162.b1.a1'], 'contains': ['648.a1.a1', '648.e1.a1', '648.i1.a1', '648.i1.b1', '648.m1.a1', '1620.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1188, -1, 6775, -1, 7857, -1, 7330, -1], 'generators': [21, 64, 80, 82, 8640, 160], 'label': '51840.cr.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '324.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462097
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '162.c1.a1'], 'contains': ['648.c1.a1', '648.n1.a1', '648.n1.b1', '1620.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [664, -1, 9220, -1, 9600, -1, 9934, -1], 'generators': [20, 160, 64, 40, 8640, 80], 'label': '51840.cr.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462098
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['12960.j1.a1', '12960.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.i1.a1', '20.k1.a1', '324.k1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [898, 7368, 8649, 8924, 9404, 1842, 9512, 2574], 'generators': [5760, 24000, 8642, 64, 80, 34880, 20, 40, 160, 17280], 'label': '51840.cr.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462099
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '162.c1.a1'], 'contains': ['648.c1.a1', '648.o1.a1', '648.o1.b1', '1620.e1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [172, -1, 9543, -1, 9357, -1, 9361, -1], 'generators': [182, 64, 200, 80, 8640, 160], 'label': '51840.cr.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462100
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '162.a1.a1', '162.d1.a1', '162.d1.b1'], 'contains': ['648.f1.a1', '648.g1.a1', '1620.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2104, -1, 7905, -1, 8461, -1, 7961, -1], 'generators': [1, 64, 2, 80, 40, 160], 'label': '51840.cr.324.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.a1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462101
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '162.a1.a1', '162.d1.c1', '162.d1.d1'], 'contains': ['648.f1.b1', '648.g1.a1', '1620.f1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2104, -1, 7989, -1, 8461, -1, 8046, -1], 'generators': [8641, 64, 2, 80, 40, 160], 'label': '51840.cr.324.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.f1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.b1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462102
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '162.a1.a1'], 'contains': ['648.f1.a1', '648.f1.b1', '648.h1.a1', '1620.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [3285, -1, 6529, -1, 7729, -1, 6954, -1], 'generators': [1, 64, 2, 80, 8680, 160], 'label': '51840.cr.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1.a1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462103
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '162.b1.a1', '162.d1.a1', '162.d1.c1'], 'contains': ['648.g1.a1', '648.i1.a1', '1620.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [773, -1, 8449, -1, 8946, -1, 8359, -1], 'generators': [21, 64, 82, 80, 40, 160], 'label': '51840.cr.324.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.a1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462104
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '162.b1.a1', '162.d1.b1', '162.d1.d1'], 'contains': ['648.g1.a1', '648.i1.b1', '1620.h1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [773, -1, 8322, -1, 8946, -1, 8545, -1], 'generators': [8661, 64, 82, 80, 40, 160], 'label': '51840.cr.324.h1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.b1', 'subgroup_fusion': None, 'weyl_group': '160.68'}
  • id: 223462105
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '162.c1.a1', '162.d1.a1', '162.d1.d1'], 'contains': ['648.g1.a1', '648.n1.a1', '648.o1.b1', '1620.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [340, -1, 9432, -1, 9485, -1, 9078, -1], 'generators': [20, 64, 40, 80, 2, 160], 'label': '51840.cr.324.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462106
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '162.c1.a1', '162.d1.b1', '162.d1.c1'], 'contains': ['648.g1.a1', '648.n1.b1', '648.o1.a1', '1620.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [340, -1, 9347, -1, 9485, -1, 9220, -1], 'generators': [8660, 64, 40, 80, 2, 160], 'label': '51840.cr.324.i1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462107
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '162.b1.a1'], 'contains': ['648.h1.a1', '648.i1.a1', '648.i1.b1', '1620.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [1064, -1, 7587, -1, 8546, -1, 7599, -1], 'generators': [21, 64, 82, 80, 8680, 160], 'label': '51840.cr.324.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '324.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1.a1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462108
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '162.c1.a1'], 'contains': ['648.k1.a1', '648.n1.a1', '648.o1.a1', '1620.k1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [443, -1, 9121, -1, 9715, -1, 9777, -1], 'generators': [20, 64, 40, 80, 8642, 160], 'label': '51840.cr.324.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462109
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['12960.j1.a1', '12960.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.f1.a1', '8.h1.b1', '8.i1.b1', '20.k1.b1', '324.k1.b1'], 'core': '4.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [898, 7368, 9445, 8311, 9404, 1842, 9379, 1060], 'generators': [5760, 960, 8642, 64, 80, 12800, 182, 200, 160, 17280], 'label': '51840.cr.4.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.b1', '8.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.b1', 'projective_image': '51840.cr', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462110
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '162.c1.a1'], 'contains': ['648.k1.a1', '648.n1.b1', '648.o1.b1', '1620.k1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [443, -1, 9681, -1, 9715, -1, 9663, -1], 'generators': [182, 64, 200, 80, 8642, 160], 'label': '51840.cr.324.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.k1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462111
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '180.a1.a1', '180.b1.a1', '180.c1.a1'], 'contains': ['720.b1.a1', '720.c1.a1', '720.d1.a1', '720.g1.a1', '720.h1.a1', '720.k1.a1', '720.l1.a1', '3240.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4918, -1, 4680, -1, 5311, -1, 5052, -1], 'generators': [8640, 6720, 8000, 2, 80, 160], 'label': '51840.cr.360.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462112
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '180.a1.a1'], 'contains': ['720.b1.a1', '720.e1.a1', '720.i1.a1', '720.i1.b1', '720.r1.a1', '1080.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [6672, -1, 3251, -1, 2970, -1, 3590, -1], 'generators': [1, 18240, 2240, 8640, 160, 2], 'label': '51840.cr.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '360.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 223462113
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '180.b1.a1'], 'contains': ['720.b1.a1', '720.f1.a1', '720.j1.a1', '720.j1.b1', '720.s1.a1', '3240.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7234, -1, 2489, -1, 2804, -1, 3306, -1], 'generators': [1, 6720, 1280, 8640, 160, 2], 'label': '51840.cr.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 223462114
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '180.c1.a1'], 'contains': ['720.c1.a1', '720.m1.a1', '720.n1.a1', '3240.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2639, -1, 7222, -1, 7081, -1, 6862, -1], 'generators': [8640, 6720, 8000, 40, 80, 160], 'label': '51840.cr.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462115
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1.a1', '180.c1.a1'], 'contains': ['720.c1.a1', '720.o1.a1', '720.p1.a1', '3240.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3453, -1, 6812, -1, 6971, -1, 6611, -1], 'generators': [8640, 6720, 8000, 42, 80, 160], 'label': '51840.cr.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462116
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.f1.a1'], 'contains': ['720.d2.a1', '720.q1.a1', '720.q1.b1', '3240.e1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [1789, -1, 6057, -1, 6113, -1, 6124, -1], 'generators': [21, 41280, 36800, 8640, 82, 160], 'label': '51840.cr.360.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '360.f1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462117
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.g1.a1', '180.a1.a1', '180.d1.a1', '180.e1.a1'], 'contains': ['720.g1.a1', '720.i1.a1', '3240.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4248, -1, 4983, -1, 5649, -1, 5390, -1], 'generators': [1, 18240, 17600, 80, 2, 160], 'label': '51840.cr.360.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462118
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.g1.b1', '180.a1.a1', '180.d1.b1', '180.e1.b1'], 'contains': ['720.g1.a1', '720.i1.b1', '3240.f1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4248, -1, 5113, -1, 5649, -1, 5650, -1], 'generators': [8641, 18240, 17600, 80, 2, 160], 'label': '51840.cr.360.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.g1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.b1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462119
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.g1.a1', '180.b1.a1', '180.d1.a1', '180.e1.b1'], 'contains': ['720.g1.a1', '720.j1.a1', '3240.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4061, -1, 5241, -1, 5502, -1, 5520, -1], 'generators': [1, 6720, 1280, 80, 2, 160], 'label': '51840.cr.360.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462120
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.h1.a1', '4.j1.a1', '10.a1.a1', '162.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3102, 3699, 7452, 2961, 7459, 4614, 7358, 7033], 'generators': [41280, 17280, 8000, 8640, 160, 2, 64, 1, 40, 80, 23040], 'label': '51840.cr.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.d1.a1', '4.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462121
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.j1.a1', '8.l1.a1', '8.l1.b1', '8.n1.a1', '20.b1.a1', '324.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4616, -1, 5405, -1, 5320, -1, 5156, -1], 'generators': [23040, 41280, 8640, 64, 2, 8000, 1, 80, 160, 17280], 'label': '51840.cr.4.h1.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.h1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462122
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.g1.b1', '180.b1.a1', '180.d1.b1', '180.e1.a1'], 'contains': ['720.g1.a1', '720.j1.b1', '3240.f1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4061, -1, 5419, -1, 5502, -1, 5780, -1], 'generators': [8641, 6720, 1280, 80, 2, 160], 'label': '51840.cr.360.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.h1.b1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462196
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.d1', '162.d1.d1', '405.a1.a1'], 'contains': ['1620.f1.b1', '1620.h1.b1', '1620.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [778, -1, 8903, -1, 9229, -1, 8736, -1], 'generators': [8641, 20], 'label': '51840.cr.810.d1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.d1.d1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.d1.d1', 'subgroup_fusion': None, 'weyl_group': '32.13'}
  • id: 223462123
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.h1.a1', '180.c1.a1', '180.d1.a1', '180.d1.b1'], 'contains': ['720.g1.a1', '720.m1.a1', '720.p1.a1', '3240.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2822, -1, 7126, -1, 7301, -1, 6765, -1], 'generators': [2, 6720, 11840, 40, 80, 160], 'label': '51840.cr.360.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462124
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.i1.a1', '180.c1.a1', '180.e1.a1', '180.e1.b1'], 'contains': ['720.g1.a1', '720.n1.a1', '720.o1.a1', '3240.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3337, -1, 6366, -1, 6688, -1, 6486, -1], 'generators': [8680, 6720, 8000, 2, 80, 160], 'label': '51840.cr.360.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462125
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.k1.a1', '180.a1.a1'], 'contains': ['720.h1.a1', '720.i1.a1', '720.i1.b1', '3240.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [5793, -1, 3939, -1, 4410, -1, 4205, -1], 'generators': [1, 18240, 17600, 8720, 2, 160], 'label': '51840.cr.360.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '360.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 223462126
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.k1.a1', '180.b1.a1'], 'contains': ['720.h1.a1', '720.j1.a1', '720.j1.b1', '3240.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [5639, -1, 3812, -1, 4263, -1, 4075, -1], 'generators': [1, 6720, 11840, 8720, 2, 160], 'label': '51840.cr.360.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '360.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 223462127
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.l1.a1', '180.c1.a1'], 'contains': ['720.k1.a1', '720.m1.a1', '720.o1.a1', '3240.k1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2973, -1, 6908, -1, 7191, -1, 7046, -1], 'generators': [8642, 6720, 8000, 40, 80, 160], 'label': '51840.cr.360.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.m1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462128
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '360.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.m1.a1', '180.c1.a1'], 'contains': ['720.k1.a1', '720.n1.a1', '720.p1.a1', '3240.l1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3089, -1, 7031, -1, 6861, -1, 6332, -1], 'generators': [8680, 6720, 8000, 42, 80, 160], 'label': '51840.cr.360.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '360.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.n1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462129
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '405.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '81.a1.a1'], 'contains': ['810.a1.a1', '810.b1.a1', '810.c1.a1', '810.d1.a1', '810.d1.b1', '810.d1.c1', '810.d1.d1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [925, -1, 8878, -1, 9451, -1, 8947, -1], 'generators': [1, 20, 8640], 'label': '51840.cr.405.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '405.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '405.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.13'}
  • id: 223462130
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.a1.a1', '240.a1.a1'], 'contains': ['960.a1.a1', '960.b1.a1', '960.c1.a1', '1440.a1.a1', '1440.a2.a1', '1440.a3.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [6813, -1, 2822, -1, 1602, -1, 1440, -1], 'generators': [8640, 23040, 160, 8000, 41280], 'label': '51840.cr.480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462131
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.d1.a1', '240.a1.a1'], 'contains': ['960.a1.a1', '960.d1.a1', '960.f1.a1', '1440.b1.a1', '1440.c1.a1', '1440.c2.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7510, -1, 1810, -1, 913, -1, 540, -1], 'generators': [8640, 8000, 2, 24000, 5760], 'label': '51840.cr.480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 223462132
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.k1.a1', '8.m1.a1', '8.m1.b1', '8.o1.a1', '20.d1.a1', '324.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1993, -1, 6713, -1, 6685, -1, 6001, -1], 'generators': [5760, 29760, 8640, 64, 82, 40640, 21, 80, 160, 17280], 'label': '51840.cr.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462133
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.d1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1'], 'contains': ['960.a1.a1', '960.e1.a1', '960.g1.a1', '1440.c1.a1', '1440.c2.a1', '1440.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7770, -1, 1407, -1, 1322, -1, 812, -1], 'generators': [8640, 6720, 2, 17280, 8000], 'label': '51840.cr.480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '480.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 223462134
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.e1.a1', '240.a1.a1', '240.d1.a1', '240.d1.b1'], 'contains': ['960.b1.a1', '960.d1.a1', '960.e1.a1', '1440.e1.a1', '1440.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8381, -1, 1237, -1, 1458, -1, 1568, -1], 'generators': [2, 17280, 160, 8000, 6720], 'label': '51840.cr.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462135
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.f1.a1', '240.a1.a1'], 'contains': ['960.b1.a1', '960.f1.a1', '960.g1.a1', '1440.g1.a1', '1440.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9581, -1, 1120, -1, 212, -1, 1080, -1], 'generators': [8642, 17280, 160, 8000, 6720], 'label': '51840.cr.480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462136
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.i1.a1', '240.a1.a1'], 'contains': ['960.c1.a1', '960.d1.a1', '960.g1.a1', '1440.m1.a1', '1440.n1.a1', '1440.n2.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8557, -1, 783, -1, 347, -1, 932, -1], 'generators': [8800, 5760, 2, 8000, 24000], 'label': '51840.cr.480.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462137
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.i1.a1', '240.a1.a1', '240.e1.a1', '240.e1.b1'], 'contains': ['960.c1.a1', '960.e1.a1', '960.f1.a1', '1440.n1.a1', '1440.n2.a1', '1440.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8699, -1, 637, -1, 760, -1, 1199, -1], 'generators': [8800, 17280, 2, 8000, 41280], 'label': '51840.cr.480.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.g1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462138
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.j1.a1', '240.b1.a1', '240.d1.a1', '240.e1.a1'], 'contains': ['960.e1.a1', '1440.q1.a1', '4320.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7927, -1, 1666, -1, 1916, -1, 2222, -1], 'generators': [1, 6720, 17280, 2, 1280], 'label': '51840.cr.480.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 223462139
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.j1.b1', '240.b1.a1', '240.d1.b1', '240.e1.b1'], 'contains': ['960.e1.a1', '1440.q1.b1', '4320.h1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7927, -1, 2145, -1, 1916, -1, 2647, -1], 'generators': [8641, 6720, 17280, 2, 1280], 'label': '51840.cr.480.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '480.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.h1.b1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 223462140
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.j1.a1', '240.c1.a1', '240.d1.a1', '240.e1.b1'], 'contains': ['960.e1.a1', '1440.q1.a1', '4320.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8112, -1, 1542, -1, 1772, -1, 2095, -1], 'generators': [1, 40320, 2, 1280, 6720], 'label': '51840.cr.480.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '480.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.i1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462141
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '480.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8640.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.j1.b1', '240.c1.a1', '240.d1.b1', '240.e1.a1'], 'contains': ['960.e1.a1', '1440.q1.b1', '4320.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8112, -1, 2270, -1, 1772, -1, 2349, -1], 'generators': [8641, 40320, 2, 1280, 6720], 'label': '51840.cr.480.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '480.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.i1.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462142
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '320.a1.a1', '320.b1.a1', '320.c1.a1', '320.d1.a1', '320.e1.a1'], 'contains': ['1920.a1.a1'], 'core': '640.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9368, 2551, 309, 2139, 626, 6760, 23, 7066], 'generators': [8000, 6720, 5760, 17280], 'label': '51840.cr.640.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '640.a1.a1', 'normal_contained_in': ['128.a1.a1', '320.a1.a1', '320.b1.a1', '320.c1.a1'], 'normal_contains': ['51840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '640.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '320.186', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '640.a1.a1', 'subgroup_fusion': None, 'weyl_group': '320.186'}
  • id: 223462143
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.e1.a1', '8.l1.a1', '8.l1.b1', '20.g1.a1', '324.g1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3625, -1, 5808, -1, 6491, -1, 5792, -1], 'generators': [23040, 41280, 8680, 64, 80, 8000, 1, 2, 160, 17280], 'label': '51840.cr.4.j1.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.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462144
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '324.a1.a1', '324.b1.a1', '324.c1.a1'], 'contains': ['1296.a1.a1', '1296.b1.a1', '1296.c1.a1', '1296.e1.a1', '1296.f1.a1', '1296.h1.a1', '1296.i1.a1', '3240.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3670, -1, 5808, -1, 6454, -1, 5863, -1], 'generators': [8640, 80, 160, 2, 64], 'label': '51840.cr.648.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462145
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '324.a1.a1'], 'contains': ['1296.a1.a1', '1296.d1.a1', '1296.g1.a1', '1296.g1.b1', '1296.o1.a1', '3240.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5955, -1, 3890, -1, 4549, -1, 3994, -1], 'generators': [1, 160, 2, 8640, 64], 'label': '51840.cr.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1.a1', 'old_label': '648.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462146
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '324.b1.a1', '324.d1.a1', '324.e1.a1'], 'contains': ['1296.b1.a1', '1296.j1.a1', '1296.k1.a1', '3240.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1342, -1, 8579, -1, 8686, -1, 8368, -1], 'generators': [8640, 64, 80, 40, 160], 'label': '51840.cr.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462147
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '324.b1.a1'], 'contains': ['1296.b1.a1', '1296.l1.a1', '1296.m1.a1', '3240.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2469, -1, 7709, -1, 8552, -1, 7792, -1], 'generators': [8640, 80, 160, 42, 64], 'label': '51840.cr.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462148
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '324.c1.a1'], 'contains': ['1296.c1.a1', '1296.n1.a1', '1296.n1.b1', '3240.e1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [1024, -1, 6641, -1, 7498, -1, 6843, -1], 'generators': [21, 82, 160, 8640, 64], 'label': '51840.cr.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '648.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462149
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '324.a1.a1', '324.f1.a1', '324.g1.a1'], 'contains': ['1296.e1.a1', '1296.g1.a1', '3240.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [3866, -1, 5916, -1, 6329, -1, 6084, -1], 'generators': [1, 2, 160, 80, 64], 'label': '51840.cr.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '648.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462150
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '324.a1.a1', '324.f1.b1', '324.g1.a1'], 'contains': ['1296.e1.a1', '1296.g1.b1', '3240.f1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [3866, -1, 5981, -1, 6329, -1, 6149, -1], 'generators': [8641, 2, 160, 80, 64], 'label': '51840.cr.648.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '648.f1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.b1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462151
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '324.b1.a1', '324.f1.a1', '324.f1.b1', '324.h1.a1', '324.h1.b1', '324.i1.a1', '324.i1.b1'], 'contains': ['1296.e1.a1', '1296.j1.a1', '1296.m1.a1', '3240.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1670, -1, 8288, -1, 8951, -1, 8259, -1], 'generators': [2, 80, 160, 40, 64], 'label': '51840.cr.648.g1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462152
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '324.b1.a1', '324.g1.a1', '324.j1.a1'], 'contains': ['1296.e1.a1', '1296.k1.a1', '1296.l1.a1', '3240.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2797, -1, 7547, -1, 8177, -1, 7588, -1], 'generators': [8680, 80, 160, 2, 64], 'label': '51840.cr.648.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462153
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '324.c1.a1', '324.h1.a1', '324.j1.a1'], 'contains': ['1296.e1.a1', '1296.n1.a1', '3240.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [659, -1, 6913, -1, 7829, -1, 7039, -1], 'generators': [21, 82, 160, 80, 64], 'label': '51840.cr.648.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '648.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1.a1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462154
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '8.m1.a1', '8.m1.b1', '20.j1.a1', '324.j1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2322, -1, 6971, -1, 7815, -1, 6556, -1], 'generators': [23040, 12480, 8680, 64, 80, 2240, 21, 82, 160, 17280], 'label': '51840.cr.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462155
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '324.c1.a1', '324.h1.b1', '324.j1.a1'], 'contains': ['1296.e1.a1', '1296.n1.b1', '3240.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [659, -1, 7025, -1, 7829, -1, 7396, -1], 'generators': [8661, 82, 160, 80, 64], 'label': '51840.cr.648.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '648.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1.b1', 'subgroup_fusion': None, 'weyl_group': '80.31'}
  • id: 223462156
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '324.a1.a1'], 'contains': ['1296.f1.a1', '1296.g1.a1', '1296.g1.b1', '3240.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5154, -1, 4855, -1, 5761, -1, 4336, -1], 'generators': [1, 2, 160, 8720, 64], 'label': '51840.cr.648.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1.a1', 'old_label': '648.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462157
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '324.b1.a1', '324.k1.a1', '324.k1.b1'], 'contains': ['1296.h1.a1', '1296.j1.a1', '1296.l1.a1', '3240.k1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1788, -1, 8185, -1, 8840, -1, 8638, -1], 'generators': [8642, 80, 160, 40, 64], 'label': '51840.cr.648.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462158
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '324.b1.a1'], 'contains': ['1296.h1.a1', '1296.k1.a1', '1296.m1.a1', '3240.l1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2174, -1, 7978, -1, 8320, -1, 7489, -1], 'generators': [8680, 80, 160, 42, 64], 'label': '51840.cr.648.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462159
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '324.c1.a1'], 'contains': ['1296.i1.a1', '1296.n1.a1', '1296.n1.b1', '3240.m1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [1997, -1, 6502, -1, 7626, -1, 6650, -1], 'generators': [21, 82, 160, 8720, 64], 'label': '51840.cr.648.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '648.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462160
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '324.d1.a1', '324.i1.a1', '324.k1.a1'], 'contains': ['1296.j1.a1', '3240.n1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [432, -1, 9199, -1, 9491, -1, 9753, -1], 'generators': [20, 40, 80, 64, 160], 'label': '51840.cr.648.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462161
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '324.d1.a1', '324.i1.b1', '324.k1.b1'], 'contains': ['1296.j1.a1', '3240.n1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [432, -1, 9535, -1, 9491, -1, 9661, -1], 'generators': [8660, 40, 80, 64, 160], 'label': '51840.cr.648.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.n1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462162
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '324.e1.a1', '324.i1.b1', '324.k1.a1'], 'contains': ['1296.j1.a1', '3240.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [261, -1, 9361, -1, 9382, -1, 9296, -1], 'generators': [8822, 80, 160, 200, 64], 'label': '51840.cr.648.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462163
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '324.e1.a1', '324.i1.a1', '324.k1.b1'], 'contains': ['1296.j1.a1', '3240.o1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [261, -1, 9627, -1, 9382, -1, 9210, -1], 'generators': [182, 80, 160, 200, 64], 'label': '51840.cr.648.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.o1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462164
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1'], 'contains': ['1440.a1.a1', '1440.c1.a1', '1440.c2.a1', '1440.e1.a1', '1440.g1.a1', '1440.n1.a1', '1440.n2.a1', '2160.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [8202, -1, 1209, -1, 1191, -1, 1316, -1], 'generators': [8640, 18240, 2, 160, 8000], 'label': '51840.cr.720.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '720.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462165
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '10.d1.a1', '10.d1.b1', '10.d1.c1', '10.d1.d1', '405.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1403, -1, 8266, -1, 8464, -1, 8426, -1], 'generators': [1, 6720, 40, 80, 23040, 20, 2, 1280, 160, 17280, 8640], 'label': '51840.cr.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462166
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '360.a1.a1', '360.b1.a1', '360.c1.a1'], 'contains': ['1440.a2.a1', '1440.b1.a1', '1440.d1.a1', '1440.f1.a1', '1440.h1.a1', '1440.m1.a1', '1440.o1.a1', '2160.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8350, -1, 2300, -1, 2359, -1, 1696, -1], 'generators': [8640, 6720, 2, 160, 8000], 'label': '51840.cr.720.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462167
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '360.a1.a1', '360.d1.a1', '360.e1.a1'], 'contains': ['1440.a2.a1', '1440.i1.a1', '1440.j1.a1', '6480.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5355, -1, 4732, -1, 5492, -1, 5172, -1], 'generators': [8640, 6720, 80, 160, 11840], 'label': '51840.cr.720.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462168
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1.a1', '360.a1.a1'], 'contains': ['1440.a2.a1', '1440.k1.a1', '1440.l1.a1', '6480.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4987, -1, 4511, -1, 4330, -1, 4749, -1], 'generators': [8640, 6720, 82, 160, 8000], 'label': '51840.cr.720.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462169
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.d2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1.a1', '360.f1.a1'], 'contains': ['1440.a3.a1', '1440.k2.a1', '1440.l2.a1', '6480.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [3976, -1, 4980, -1, 4855, -1, 4891, -1], 'generators': [8640, 41280, 82, 160, 12800], 'label': '51840.cr.720.d2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '720.d2.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.d2.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462170
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '360.b1.a1'], 'contains': ['1440.b1.a1', '1440.p1.a1', '1440.p1.b1', '2160.b1.a1', '2160.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6627, -1, 3322, -1, 2817, -1, 3344, -1], 'generators': [1, 18240, 8640, 2240, 2], 'label': '51840.cr.720.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '720.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462171
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '240.c1.a1', '360.c1.a1'], 'contains': ['1440.d1.a1', '1440.q1.a1', '1440.q1.b1', '6480.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7279, -1, 2007, -1, 2547, -1, 2790, -1], 'generators': [1, 6720, 8640, 2, 1280], 'label': '51840.cr.720.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '720.f1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 223462172
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.g1.a1', '360.a1.a1', '360.g1.a1', '360.g1.b1', '360.h1.a1', '360.h1.b1', '360.i1.a1', '360.j1.a1'], 'contains': ['1440.f1.a1', '1440.i1.a1', '1440.k1.a1', '6480.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4279, -1, 5422, -1, 5684, -1, 5595, -1], 'generators': [2, 6720, 80, 160, 8000], 'label': '51840.cr.720.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.g1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462173
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.h1.a1', '360.a1.a1', '360.k1.a1', '360.l1.a1'], 'contains': ['1440.f1.a1', '1440.j1.a1', '1440.l1.a1', '6480.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5689, -1, 4041, -1, 4138, -1, 4232, -1], 'generators': [8720, 6720, 2, 160, 11840], 'label': '51840.cr.720.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462174
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.i1.a1', '360.b1.a1', '360.g1.a1', '360.k1.a1'], 'contains': ['1440.f1.a1', '1440.p1.a1', '2160.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7147, -1, 3170, -1, 3123, -1, 3555, -1], 'generators': [1, 18240, 160, 2, 2240], 'label': '51840.cr.720.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '720.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 223462175
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.i1.b1', '360.b1.a1', '360.g1.b1', '360.k1.a1'], 'contains': ['1440.f1.a1', '1440.p1.b1', '2160.d1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7147, -1, 3556, -1, 3123, -1, 3870, -1], 'generators': [8641, 18240, 160, 2, 2240], 'label': '51840.cr.720.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.a1.a1', 'old_label': '720.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.i1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 223462176
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '40.c1.a1', '648.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4616, 2715, 4878, 2287, 5480, 7410, 4885, 7732], 'generators': [17280, 5760, 2, 11840, 160, 41280, 8640, 80, 64], 'label': '51840.cr.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462177
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '360.c1.a1', '360.h1.a1', '360.l1.a1'], 'contains': ['1440.f1.a1', '1440.q1.a1', '6480.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7013, -1, 2602, -1, 2997, -1, 2988, -1], 'generators': [1, 6720, 160, 2, 1280], 'label': '51840.cr.720.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '720.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 223462178
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.b1', '360.c1.a1', '360.h1.b1', '360.l1.a1'], 'contains': ['1440.f1.a1', '1440.q1.b1', '6480.g1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 180, 'diagramx': [7013, -1, 2463, -1, 2997, -1, 3131, -1], 'generators': [8641, 6720, 160, 2, 1280], 'label': '51840.cr.720.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '180.b1.a1', 'old_label': '720.j1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.j1.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 223462179
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.j1.a1', '360.a1.a1', '360.m1.a1', '360.n1.a1'], 'contains': ['1440.h1.a1', '1440.i1.a1', '1440.l1.a1', '6480.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4613, -1, 5174, -1, 5331, -1, 5314, -1], 'generators': [8642, 6720, 80, 160, 8000], 'label': '51840.cr.720.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.k1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462180
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.k1.a1', '360.a1.a1'], 'contains': ['1440.h1.a1', '1440.j1.a1', '1440.k1.a1', '6480.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4817, -1, 4263, -1, 4491, -1, 4606, -1], 'generators': [8720, 6720, 82, 160, 11840], 'label': '51840.cr.720.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462181
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a1', '360.d1.a1', '360.i1.a1', '360.m1.a1'], 'contains': ['1440.i1.a1', '6480.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2723, -1, 7228, -1, 7305, -1, 6719, -1], 'generators': [40, 6720, 80, 160, 8000], 'label': '51840.cr.720.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.m1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462182
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a1', '360.d1.a1', '360.j1.a1', '360.n1.a1'], 'contains': ['1440.i1.a1', '6480.k1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [2949, -1, 6825, -1, 6697, -1, 6403, -1], 'generators': [8680, 6720, 80, 160, 8000], 'label': '51840.cr.720.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.n1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462183
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.l1.a1', '360.e1.a1', '360.j1.a1', '360.m1.a1'], 'contains': ['1440.i1.a1', '6480.l1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3204, -1, 6346, -1, 7126, -1, 6514, -1], 'generators': [8682, 6720, 80, 160, 8000], 'label': '51840.cr.720.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.o1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462184
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.m1.a1', '360.e1.a1', '360.i1.a1', '360.n1.a1'], 'contains': ['1440.i1.a1', '6480.m1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [3044, -1, 7148, -1, 7184, -1, 6459, -1], 'generators': [42, 6720, 80, 160, 8000], 'label': '51840.cr.720.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '720.p1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.p1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462185
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.n1.a1', '360.f1.a1'], 'contains': ['1440.k2.a1', '6480.n1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [1554, -1, 6109, -1, 6123, -1, 6236, -1], 'generators': [21, 41280, 82, 160, 36800], 'label': '51840.cr.720.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '720.q1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.q1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462186
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.n1.b1', '360.f1.a1'], 'contains': ['1440.k2.a1', '6480.n1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [1554, -1, 6187, -1, 6123, -1, 6288, -1], 'generators': [8661, 41280, 82, 160, 36800], 'label': '51840.cr.720.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '720.q1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.q1.b1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462187
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.i1.a1', '40.a1.a1', '648.c1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2681, 8559, 7947, 6566, 7844, 2553, 8117, 2792], 'generators': [17280, 5760, 40, 8000, 80, 6720, 8640, 64, 160], 'label': '51840.cr.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.b1.a1', '16.i1.a1', '16.h1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462188
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.o1.a1', '360.b1.a1'], 'contains': ['1440.m1.a1', '1440.p1.a1', '1440.p1.b1', '2160.e1.a1', '2160.e1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8044, -1, 2901, -1, 2673, -1, 3243, -1], 'generators': [1, 18240, 8800, 2, 2240], 'label': '51840.cr.720.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '720.r1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.r1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462189
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '720.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.e1.a1', '240.e1.b1', '360.c1.a1'], 'contains': ['1440.o1.a1', '1440.q1.a1', '1440.q1.b1', '6480.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [7648, -1, 1651, -1, 2203, -1, 2477, -1], 'generators': [1, 6720, 8800, 2, 1280], 'label': '51840.cr.720.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.c1.a1', 'old_label': '720.s1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.s1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 223462190
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '162.a1.a1', '405.a1.a1'], 'contains': ['1620.a1.a1', '1620.b1.a1', '1620.f1.a1', '1620.f1.b1', '1620.g1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2640, -1, 7716, -1, 8251, -1, 7829, -1], 'generators': [1, 8640, 40], 'label': '51840.cr.810.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462191
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '162.b1.a1', '405.a1.a1'], 'contains': ['1620.b1.a1', '1620.c1.a1', '1620.h1.a1', '1620.h1.b1', '1620.j1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [1229, -1, 8354, -1, 9051, -1, 8452, -1], 'generators': [21, 8640, 40], 'label': '51840.cr.810.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462192
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '162.c1.a1', '405.a1.a1'], 'contains': ['1620.b1.a1', '1620.d1.a1', '1620.e1.a1', '1620.i1.a1', '1620.i1.b1', '1620.k1.a1', '1620.k1.b1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [246, -1, 9564, -1, 9917, -1, 9511, -1], 'generators': [20, 8640, 2], 'label': '51840.cr.810.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462193
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.a1', '162.d1.a1', '405.a1.a1'], 'contains': ['1620.f1.a1', '1620.h1.a1', '1620.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [778, -1, 8734, -1, 9229, -1, 8650, -1], 'generators': [1, 20], 'label': '51840.cr.810.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.13'}
  • id: 223462194
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.b1', '162.d1.b1', '405.a1.a1'], 'contains': ['1620.f1.a1', '1620.h1.b1', '1620.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [778, -1, 9039, -1, 9229, -1, 8936, -1], 'generators': [1, 8660], 'label': '51840.cr.810.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.d1.b1', 'subgroup_fusion': None, 'weyl_group': '32.13'}
  • id: 223462195
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '810.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.d1.c1', '162.d1.c1', '405.a1.a1'], 'contains': ['1620.f1.b1', '1620.h1.a1', '1620.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [778, -1, 8818, -1, 9229, -1, 8822, -1], 'generators': [8641, 8660], 'label': '51840.cr.810.d1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '810.d1.c1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '810.d1.c1', 'subgroup_fusion': None, 'weyl_group': '32.13'}
  • id: 223462197
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.a1.a1', '480.a1.a1', '480.b1.a1', '480.c1.a1'], 'contains': ['1920.a1.a1', '2880.a1.a1', '2880.a2.a1', '2880.a3.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7408, -1, 1827, -1, 1305, -1, 343, -1], 'generators': [8640, 8000, 41280, 23040], 'label': '51840.cr.960.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '960.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462198
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.k1.a1', '40.e1.a1', '648.d1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3834, 4572, 6032, 3736, 6976, 4949, 6830, 6270], 'generators': [17280, 23040, 42, 25280, 160, 960, 8640, 80, 64], 'label': '51840.cr.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '25920.dn', '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': '25920.dn'}
  • id: 223462199
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.b1.a1', '480.a1.a1', '480.d1.a1', '480.e1.a1'], 'contains': ['1920.a1.a1', '2880.b1.a1', '2880.b2.a1', '2880.b3.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7029, -1, 2402, -1, 1617, -1, 1783, -1], 'generators': [160, 8000, 41280, 23040], 'label': '51840.cr.960.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '960.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462200
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.c1.a1', '480.a1.a1', '480.f1.a1', '480.g1.a1'], 'contains': ['1920.a1.a1', '2880.c1.a1', '2880.c2.a1', '2880.c3.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8775, -1, 924, -1, 838, -1, 836, -1], 'generators': [8800, 8000, 41280, 23040], 'label': '51840.cr.960.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '960.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 223462201
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.d1.a1', '480.b1.a1', '480.d1.a1', '480.f1.a1'], 'contains': ['1920.a1.a1', '2880.d1.a1', '2880.e1.a1', '2880.e2.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9205, -1, 615, -1, 529, -1, 680, -1], 'generators': [2, 24000, 5760, 8000], 'label': '51840.cr.960.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '960.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 223462202
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.d1.a1', '480.c1.a1', '480.d1.a1', '480.g1.a1', '480.h1.a1', '480.h1.b1', '480.i1.a1', '480.i1.b1'], 'contains': ['1920.a1.a1', '2880.e1.a1', '2880.e2.a1', '2880.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9405, -1, 500, -1, 1172, -1, 1175, -1], 'generators': [2, 17280, 8000, 6720], 'label': '51840.cr.960.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '960.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 223462203
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.e1.a1', '480.b1.a1', '480.e1.a1', '480.g1.a1'], 'contains': ['1920.a1.a1', '2880.g1.a1', '2880.h1.a1', '2880.h2.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9757, -1, 61, -1, 200, -1, 229, -1], 'generators': [8642, 24000, 5760, 8000], 'label': '51840.cr.960.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '960.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 223462204
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '960.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.e1.a1', '480.c1.a1', '480.e1.a1', '480.f1.a1'], 'contains': ['1920.a1.a1', '2880.h1.a1', '2880.h2.a1', '2880.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9970, -1, 250, -1, 331, -1, 113, -1], 'generators': [8642, 17280, 8000, 6720], 'label': '51840.cr.960.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '960.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 223462205
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '360.b1.a1'], 'contains': ['2160.a1.a1', '2160.b1.a1', '2160.c1.a1', '2160.d1.a1', '2160.d1.b1', '2160.e1.a1', '2160.e1.b1', '3240.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [6534, -1, 3547, -1, 3254, -1, 3671, -1], 'generators': [1, 18240, 8640, 160, 2], 'label': '51840.cr.1080.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '1080.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1080.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462206
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '648.a1.a1', '648.b1.a1'], 'contains': ['2592.a1.a1', '2592.b1.a1', '2592.c1.a1', '2592.d1.a1', '2592.i1.a1', '6480.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5433, -1, 4001, -1, 5031, -1, 4135, -1], 'generators': [8640, 160, 64, 2], 'label': '51840.cr.1296.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462207
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '648.a1.a1', '648.c1.a1', '648.d1.a1'], 'contains': ['2592.a1.a1', '2592.e1.a1', '2592.f1.a1', '6480.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3798, -1, 6279, -1, 6968, -1, 5808, -1], 'generators': [8640, 64, 160, 80], 'label': '51840.cr.1296.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462208
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '648.a1.a1', '648.e1.a1'], 'contains': ['2592.a1.a1', '2592.g1.a1', '2592.h1.a1', '6480.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3254, -1, 5688, -1, 6251, -1, 5376, -1], 'generators': [8640, 160, 64, 82], 'label': '51840.cr.1296.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462209
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.e1.a1', '4.e1.b1', '4.f1.a1', '4.f1.b1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.k1.a1', '40.h1.a1', '648.g1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2861, 3673, 7772, 5102, 8175, 6498, 7633, 4891], 'generators': [17280, 5760, 40, 11840, 160, 41280, 2, 80, 64], 'label': '51840.cr.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.d1.a1', '4.d1.b1', '4.e1.a1', '4.e1.b1', '4.f1.b1', '4.f1.a1'], 'normal_contains': ['16.d1.a1', '16.h1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '51840.cr', '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': '25920.dn'}
  • id: 223462210
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '648.b1.a1'], 'contains': ['2592.b1.a1', '2592.j1.a1', '2592.j1.b1', '6480.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6071, -1, 3170, -1, 3816, -1, 2444, -1], 'generators': [1, 2, 64, 8640], 'label': '51840.cr.1296.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.b1.a1', 'old_label': '1296.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462211
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '648.a1.a1', '648.f1.a1', '648.f1.b1', '648.g1.a1', '648.h1.a1', '648.i1.a1', '648.i1.b1'], 'contains': ['2592.c1.a1', '2592.e1.a1', '2592.g1.a1', '6480.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2984, -1, 6172, -1, 6813, -1, 6177, -1], 'generators': [2, 160, 64, 80], 'label': '51840.cr.1296.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462212
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '648.a1.a1', '648.j1.a1'], 'contains': ['2592.c1.a1', '2592.f1.a1', '2592.h1.a1', '6480.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4354, -1, 5052, -1, 5945, -1, 4880, -1], 'generators': [8720, 160, 64, 2], 'label': '51840.cr.1296.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.f1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462213
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '648.b1.a1', '648.f1.a1', '648.j1.a1'], 'contains': ['2592.c1.a1', '2592.j1.a1', '6480.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5559, -1, 4443, -1, 4720, -1, 4297, -1], 'generators': [1, 2, 64, 160], 'label': '51840.cr.1296.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1.a1', 'old_label': '1296.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462214
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '648.b1.a1', '648.f1.b1', '648.j1.a1'], 'contains': ['2592.c1.a1', '2592.j1.b1', '6480.g1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5559, -1, 4320, -1, 4720, -1, 4394, -1], 'generators': [8641, 2, 64, 160], 'label': '51840.cr.1296.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1.a1', 'old_label': '1296.g1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.g1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462215
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '648.a1.a1', '648.k1.a1', '648.l1.a1'], 'contains': ['2592.d1.a1', '2592.e1.a1', '2592.h1.a1', '6480.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3384, -1, 6384, -1, 6612, -1, 5916, -1], 'generators': [8642, 160, 64, 80], 'label': '51840.cr.1296.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462216
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '648.a1.a1', '648.m1.a1'], 'contains': ['2592.d1.a1', '2592.f1.a1', '2592.g1.a1', '6480.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3537, -1, 5580, -1, 6375, -1, 5266, -1], 'generators': [8720, 160, 64, 82], 'label': '51840.cr.1296.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.i1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462217
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '648.c1.a1', '648.g1.a1', '648.k1.a1', '648.n1.a1', '648.n1.b1', '648.o1.a1', '648.o1.b1'], 'contains': ['2592.e1.a1', '6480.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1453, -1, 8802, -1, 8776, -1, 8493, -1], 'generators': [40, 80, 160, 64], 'label': '51840.cr.1296.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462218
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '648.c1.a1', '648.h1.a1', '648.l1.a1'], 'contains': ['2592.e1.a1', '6480.k1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2000, -1, 7852, -1, 8157, -1, 7381, -1], 'generators': [8680, 80, 160, 64], 'label': '51840.cr.1296.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462219
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '648.d1.a1', '648.h1.a1', '648.k1.a1'], 'contains': ['2592.e1.a1', '6480.l1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2659, -1, 7406, -1, 8261, -1, 7709, -1], 'generators': [8682, 160, 64, 80], 'label': '51840.cr.1296.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.l1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462220
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.d1.a1', '16.i1.a1', '16.j1.a1', '40.i1.a1', '648.h1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3629, 6137, 5893, 3037, 6679, 4156, 6689, 5564], 'generators': [17280, 40320, 2, 29120, 160, 35520, 8680, 80, 64], 'label': '51840.cr.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.d1.a1', '16.i1.a1', '16.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462221
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '648.d1.a1', '648.g1.a1', '648.l1.a1'], 'contains': ['2592.e1.a1', '6480.m1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2203, -1, 7948, -1, 8393, -1, 7643, -1], 'generators': [42, 160, 64, 80], 'label': '51840.cr.1296.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1296.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.m1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462222
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '648.e1.a1', '648.i1.a1', '648.m1.a1'], 'contains': ['2592.g1.a1', '6480.n1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [882, -1, 6640, -1, 7456, -1, 6553, -1], 'generators': [21, 160, 64, 82], 'label': '51840.cr.1296.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '1296.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.n1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462223
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.b1', '648.e1.a1', '648.i1.b1', '648.m1.a1'], 'contains': ['2592.g1.a1', '6480.n1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [882, -1, 6754, -1, 7456, -1, 6767, -1], 'generators': [8661, 160, 64, 82], 'label': '51840.cr.1296.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '1296.n1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.n1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462224
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1296.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '648.b1.a1'], 'contains': ['2592.i1.a1', '2592.j1.a1', '2592.j1.b1', '6480.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6253, -1, 2509, -1, 3674, -1, 2347, -1], 'generators': [1, 2, 64, 8800], 'label': '51840.cr.1296.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.b1.a1', 'old_label': '1296.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.o1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462225
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '720.a1.a1'], 'contains': ['2880.a1.a1', '2880.b1.a1', '2880.c1.a1', '4320.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [7438, -1, 1801, -1, 1503, -1, 1296, -1], 'generators': [8640, 160, 8000, 18240], 'label': '51840.cr.1440.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '1440.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462226
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.a2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '720.b1.a1', '720.c1.a1', '720.d1.a1'], 'contains': ['2880.a2.a1', '2880.b2.a1', '2880.c2.a1', '4320.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6922, -1, 2953, -1, 2899, -1, 2004, -1], 'generators': [8640, 160, 8000, 6720], 'label': '51840.cr.1440.a2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.a2.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a2.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462227
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.a3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.a1.a1', '720.d2.a1'], 'contains': ['2880.a3.a1', '2880.b3.a1', '2880.c3.a1', '4320.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6680, -1, 3483, -1, 3034, -1, 2124, -1], 'generators': [8640, 160, 8000, 41280], 'label': '51840.cr.1440.a3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '1440.a3.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a3.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462228
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.b1.a1', '720.b1.a1', '720.e1.a1'], 'contains': ['2880.a2.a1', '2880.d1.a1', '2880.g1.a1', '4320.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8236, -1, 2002, -1, 2102, -1, 1505, -1], 'generators': [8640, 2, 2240, 18240], 'label': '51840.cr.1440.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462229
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.b1.a1', '480.c1.a1', '720.a1.a1'], 'contains': ['2880.a1.a1', '2880.e1.a1', '2880.h1.a1', '4320.b1.a1', '4320.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [7812, -1, 1196, -1, 939, -1, 477, -1], 'generators': [8640, 2, 18240, 8000], 'label': '51840.cr.1440.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '1440.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462230
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.c2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.b1.a1', '480.c1.a1', '720.a1.a1'], 'contains': ['2880.a1.a1', '2880.e2.a1', '2880.h2.a1', '4320.b1.a1', '4320.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [7929, -1, 1292, -1, 1049, -1, 574, -1], 'generators': [8640, 2, 24000, 8000], 'label': '51840.cr.1440.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '1440.c2.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.c2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462231
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.e1.b1', '4.i1.a1', '4.k1.a1', '10.b1.a1', '162.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2190, 5588, 7751, 3819, 8208, 6409, 7917, 6168], 'generators': [12480, 17280, 2240, 8640, 160, 82, 64, 21, 40, 80, 23040], 'label': '51840.cr.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.e1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462232
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.g1.a1', '4.g1.b1'], 'contains': ['16.f1.a1', '16.h1.a1', '16.j1.a1', '40.l1.a1', '648.k1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3470, 6933, 7632, 5820, 8012, 3400, 8266, 4167], 'generators': [17280, 5760, 40, 11840, 160, 41280, 8642, 80, 64], 'label': '51840.cr.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.a1.a1', '4.g1.b1', '4.g1.a1'], 'normal_contains': ['16.f1.a1', '16.h1.a1', '16.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462233
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.c1.a1', '720.b1.a1', '720.f1.a1'], 'contains': ['2880.a2.a1', '2880.f1.a1', '2880.i1.a1', '4320.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8342, -1, 1486, -1, 1866, -1, 937, -1], 'generators': [8640, 2, 8000, 6720], 'label': '51840.cr.1440.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '1440.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462234
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.d1.a1', '720.a1.a1'], 'contains': ['2880.b1.a1', '2880.e1.a1', '2880.e2.a1', '4320.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [8482, -1, 1120, -1, 1402, -1, 1565, -1], 'generators': [2, 160, 8000, 18240], 'label': '51840.cr.1440.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '1440.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462235
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.d1.a1', '720.b1.a1', '720.g1.a1', '720.h1.a1', '720.i1.a1', '720.i1.b1', '720.j1.a1', '720.j1.b1'], 'contains': ['2880.b2.a1', '2880.d1.a1', '2880.f1.a1', '4320.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7230, -1, 2303, -1, 2763, -1, 2895, -1], 'generators': [2, 160, 8000, 6720], 'label': '51840.cr.1440.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.f1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462236
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.e1.a1', '720.a1.a1'], 'contains': ['2880.b1.a1', '2880.h1.a1', '2880.h2.a1', '4320.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [9968, -1, 1063, -1, 432, -1, 766, -1], 'generators': [8642, 160, 8000, 18240], 'label': '51840.cr.1440.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '1440.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462237
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.e1.a1', '720.b1.a1', '720.k1.a1', '720.l1.a1'], 'contains': ['2880.b2.a1', '2880.g1.a1', '2880.i1.a1', '4320.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9329, -1, 2555, -1, 2334, -1, 1884, -1], 'generators': [8642, 160, 8000, 6720], 'label': '51840.cr.1440.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462238
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.b1.a1', '720.c1.a1', '720.g1.a1', '720.k1.a1', '720.m1.a1', '720.n1.a1', '720.o1.a1', '720.p1.a1'], 'contains': ['2880.b2.a1', '12960.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4576, -1, 5348, -1, 5773, -1, 5563, -1], 'generators': [80, 160, 11840, 6720], 'label': '51840.cr.1440.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462239
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.c1.a1', '720.c1.a1', '720.h1.a1', '720.l1.a1'], 'contains': ['2880.b2.a1', '12960.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5673, -1, 4324, -1, 4483, -1, 4515, -1], 'generators': [8720, 160, 11840, 6720], 'label': '51840.cr.1440.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.j1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462240
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.g1.a1', '720.d1.a1', '720.g1.a1', '720.l1.a1'], 'contains': ['2880.b2.a1', '12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [4216, -1, 4819, -1, 4645, -1, 5029, -1], 'generators': [82, 160, 8000, 6720], 'label': '51840.cr.1440.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.k1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462241
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.g1.a1', '720.d2.a1', '720.q1.a1', '720.q1.b1'], 'contains': ['2880.b3.a1', '12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [3685, -1, 5235, -1, 4881, -1, 5172, -1], 'generators': [82, 160, 12800, 41280], 'label': '51840.cr.1440.k2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '1440.k2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.k2.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462242
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.h1.a1', '720.d1.a1', '720.h1.a1', '720.k1.a1'], 'contains': ['2880.b2.a1', '12960.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [5109, -1, 4652, -1, 4284, -1, 4697, -1], 'generators': [8722, 160, 8000, 6720], 'label': '51840.cr.1440.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462243
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.f1.a1', '16.i1.a1', '16.k1.a1', '40.m1.a1', '648.l1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3102, 5407, 6169, 4436, 6817, 5742, 6566, 6975], 'generators': [17280, 5760, 42, 29120, 160, 35520, 8680, 80, 64], 'label': '51840.cr.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.f1.a1', '16.i1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462244
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.l2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.h1.a1', '720.d2.a1'], 'contains': ['2880.b3.a1', '12960.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [4971, -1, 4905, -1, 4384, -1, 4786, -1], 'generators': [8722, 160, 12800, 41280], 'label': '51840.cr.1440.l2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '1440.l2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.l2.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462245
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.f1.a1', '720.b1.a1', '720.r1.a1'], 'contains': ['2880.c2.a1', '2880.d1.a1', '2880.i1.a1', '4320.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8660, -1, 1603, -1, 2001, -1, 1654, -1], 'generators': [8800, 2, 2240, 18240], 'label': '51840.cr.1440.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.m1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462246
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.f1.a1', '480.g1.a1', '720.a1.a1'], 'contains': ['2880.c1.a1', '2880.e1.a1', '2880.h2.a1', '4320.f1.a1', '4320.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [9157, -1, 548, -1, 693, -1, 1027, -1], 'generators': [8800, 2, 8000, 18240], 'label': '51840.cr.1440.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '1440.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462247
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.f1.a1', '480.g1.a1', '720.a1.a1'], 'contains': ['2880.c1.a1', '2880.e2.a1', '2880.h1.a1', '4320.f1.a1', '4320.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [8892, -1, 638, -1, 759, -1, 1086, -1], 'generators': [8800, 2, 8000, 24000], 'label': '51840.cr.1440.n2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '1440.n2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.n2.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462248
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.g1.a1', '720.b1.a1', '720.s1.a1'], 'contains': ['2880.c2.a1', '2880.f1.a1', '2880.g1.a1', '4320.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9001, -1, 759, -1, 1731, -1, 1416, -1], 'generators': [8800, 2, 8000, 6720], 'label': '51840.cr.1440.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '1440.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.o1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462249
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.j1.a1', '720.e1.a1', '720.i1.a1', '720.r1.a1'], 'contains': ['2880.d1.a1', '4320.h1.a1', '4320.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8129, -1, 2755, -1, 2597, -1, 3016, -1], 'generators': [1, 2240, 2, 18240], 'label': '51840.cr.1440.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '1440.p1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462250
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.j1.b1', '720.e1.a1', '720.i1.b1', '720.r1.a1'], 'contains': ['2880.d1.a1', '4320.h1.b1', '4320.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8129, -1, 3259, -1, 2597, -1, 3535, -1], 'generators': [8641, 2240, 2, 18240], 'label': '51840.cr.1440.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '1440.p1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.p1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462251
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.h1.a1', '480.i1.a1', '720.f1.a1', '720.j1.a1', '720.s1.a1'], 'contains': ['2880.f1.a1', '12960.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7657, -1, 1383, -1, 2217, -1, 2675, -1], 'generators': [1, 2, 1280, 6720], 'label': '51840.cr.1440.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '1440.q1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.q1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 223462252
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1440.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4320.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.h1.b1', '480.i1.b1', '720.f1.a1', '720.j1.b1', '720.s1.a1'], 'contains': ['2880.f1.a1', '12960.j1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7657, -1, 1930, -1, 2217, -1, 2791, -1], 'generators': [8641, 2, 1280, 6720], 'label': '51840.cr.1440.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '1440.q1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.q1.b1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 223462253
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.b1.a1', '324.a1.a1', '810.a1.a1'], 'contains': ['3240.a1.a1', '3240.b1.a1', '3240.f1.a1', '3240.f1.b1', '3240.j1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [4660, -1, 5930, -1, 5928, -1, 5727, -1], 'generators': [1, 8640, 80], 'label': '51840.cr.1620.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.a1.a1', 'old_label': '1620.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462254
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['6480.d1.a1', '6480.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.h1.a1', '40.b1.a1', '648.n1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [903, 9325, 8730, 8938, 9502, 1130, 9956, 1526], 'generators': [17280, 40320, 64, 46400, 80, 960, 20, 40, 160], 'label': '51840.cr.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.h1.a1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462255
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.c1.a1', '324.b1.a1', '810.a1.a1', '810.b1.a1', '810.c1.a1'], 'contains': ['3240.a1.a1', '3240.c1.a1', '3240.d1.a1', '3240.g1.a1', '3240.h1.a1', '3240.k1.a1', '3240.l1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [1976, -1, 8069, -1, 9147, -1, 8125, -1], 'generators': [8640, 2, 40], 'label': '51840.cr.1620.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462256
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '324.c1.a1', '810.b1.a1'], 'contains': ['3240.a1.a1', '3240.e1.a1', '3240.i1.a1', '3240.i1.b1', '3240.m1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [1528, -1, 7064, -1, 7968, -1, 7163, -1], 'generators': [21, 8640, 80], 'label': '51840.cr.1620.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.b1.a1', 'old_label': '1620.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462257
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '324.d1.a1', '810.c1.a1'], 'contains': ['3240.c1.a1', '3240.n1.a1', '3240.n1.b1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [530, -1, 9441, -1, 9809, -1, 9934, -1], 'generators': [20, 8640], 'label': '51840.cr.1620.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1620.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462258
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.a1', '324.e1.a1', '810.c1.a1'], 'contains': ['3240.c1.a1', '3240.o1.a1', '3240.o1.b1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [296, -1, 9765, -1, 9594, -1, 9398, -1], 'generators': [182, 8640], 'label': '51840.cr.1620.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462259
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.a1', '324.f1.a1', '810.a1.a1', '810.d1.a1', '810.d1.b1'], 'contains': ['3240.f1.a1', '3240.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2573, -1, 7708, -1, 8445, -1, 7968, -1], 'generators': [1, 40], 'label': '51840.cr.1620.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462260
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.d1.b1', '324.f1.b1', '810.a1.a1', '810.d1.c1', '810.d1.d1'], 'contains': ['3240.f1.b1', '3240.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2573, -1, 7954, -1, 8445, -1, 8034, -1], 'generators': [8641, 40], 'label': '51840.cr.1620.f1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.f1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.f1.b1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462261
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.e1.b1', '324.g1.a1', '810.a1.a1'], 'contains': ['3240.f1.a1', '3240.f1.b1', '3240.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [3058, -1, 6582, -1, 7712, -1, 6573, -1], 'generators': [1, 8680], 'label': '51840.cr.1620.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.a1.a1', 'old_label': '1620.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462262
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.h1.a1', '324.h1.a1', '810.b1.a1', '810.d1.a1', '810.d1.c1'], 'contains': ['3240.g1.a1', '3240.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [978, -1, 8435, -1, 9249, -1, 8488, -1], 'generators': [21, 40], 'label': '51840.cr.1620.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462263
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.h1.b1', '324.h1.b1', '810.b1.a1', '810.d1.b1', '810.d1.d1'], 'contains': ['3240.g1.a1', '3240.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [978, -1, 8569, -1, 9249, -1, 8554, -1], 'generators': [8661, 40], 'label': '51840.cr.1620.h1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462264
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.i1.a1', '324.i1.a1', '810.c1.a1', '810.d1.a1', '810.d1.d1'], 'contains': ['3240.g1.a1', '3240.n1.a1', '3240.o1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [97, -1, 9266, -1, 9701, -1, 9040, -1], 'generators': [20, 2], 'label': '51840.cr.1620.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462265
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['6480.d1.a1', '6480.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.f1.b1', '4.g1.b1'], 'contains': ['16.h1.a1', '40.b1.b1', '648.n1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [903, 9325, 9315, 8434, 9502, 1130, 9855, 1017], 'generators': [17280, 40320, 64, 46400, 80, 960, 8660, 40, 160], 'label': '51840.cr.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.b1.a1', '4.f1.b1', '4.g1.b1'], 'normal_contains': ['16.h1.a1', '40.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462266
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.i1.b1', '324.i1.b1', '810.c1.a1', '810.d1.b1', '810.d1.c1'], 'contains': ['3240.g1.a1', '3240.n1.b1', '3240.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [97, -1, 9618, -1, 9701, -1, 9131, -1], 'generators': [8660, 2], 'label': '51840.cr.1620.i1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462267
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.j1.a1', '324.j1.a1', '810.b1.a1'], 'contains': ['3240.h1.a1', '3240.i1.a1', '3240.i1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [1174, -1, 7514, -1, 9045, -1, 7671, -1], 'generators': [21, 8680], 'label': '51840.cr.1620.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.b1.a1', 'old_label': '1620.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462268
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.k1.a1', '324.k1.a1', '810.c1.a1'], 'contains': ['3240.k1.a1', '3240.n1.a1', '3240.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [183, -1, 9534, -1, 9917, -1, 9588, -1], 'generators': [20, 8642], 'label': '51840.cr.1620.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462269
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1620.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.k1.b1', '324.k1.b1', '810.c1.a1'], 'contains': ['3240.k1.a1', '3240.n1.b1', '3240.o1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [183, -1, 9891, -1, 9917, -1, 9513, -1], 'generators': [182, 8642], 'label': '51840.cr.1620.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '1620.k1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1620.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462270
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '1920.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['640.a1.a1', '960.a1.a1', '960.b1.a1', '960.c1.a1', '960.d1.a1', '960.e1.a1', '960.f1.a1', '960.g1.a1'], 'contains': ['5760.a1.a1', '5760.a2.a1', '5760.a3.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9746, -1, 78, -1, 922, -1, 738, -1], 'generators': [8000, 41280, 23040], 'label': '51840.cr.1920.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '640.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '1920.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1920.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 223462271
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.a1.a1', '720.b1.a1', '1080.a1.a1'], 'contains': ['4320.a1.a1', '4320.b1.a1', '4320.c1.a1', '4320.d1.a1', '4320.e1.a1', '4320.f1.a1', '4320.g1.a1', '6480.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7039, -1, 3343, -1, 2465, -1, 2241, -1], 'generators': [8640, 2, 160, 8000], 'label': '51840.cr.2160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '2160.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462272
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '720.e1.a1', '1080.a1.a1'], 'contains': ['4320.b1.a1', '4320.h1.a1', '4320.h1.b1', '6480.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [6331, -1, 3816, -1, 3587, -1, 3654, -1], 'generators': [1, 8640, 35840, 2], 'label': '51840.cr.2160.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '2160.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462273
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.c1.a1', '720.e1.a1', '1080.a1.a1'], 'contains': ['4320.b1.a1', '4320.i1.a1', '4320.i1.b1', '6480.d1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6473, -1, 3699, -1, 3342, -1, 3262, -1], 'generators': [1, 8640, 2, 18240], 'label': '51840.cr.2160.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '2160.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462274
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.a1', '720.i1.a1', '1080.a1.a1'], 'contains': ['4320.d1.a1', '4320.h1.a1', '4320.i1.a1', '6480.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7263, -1, 3132, -1, 3465, -1, 3790, -1], 'generators': [1, 160, 2, 18240], 'label': '51840.cr.2160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '2160.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462275
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.d1.b1', '720.i1.b1', '1080.a1.a1'], 'contains': ['4320.d1.a1', '4320.h1.b1', '4320.i1.b1', '6480.g1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7263, -1, 4030, -1, 3465, -1, 3888, -1], 'generators': [8641, 160, 2, 18240], 'label': '51840.cr.2160.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '2160.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462276
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['6480.d1.a1', '6480.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.b1', '4.g1.a1'], 'contains': ['16.h1.a1', '40.o1.a1', '648.o1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [556, 7729, 9151, 7874, 9037, 1764, 9360, 3494], 'generators': [17280, 23040, 200, 12800, 160, 960, 8822, 80, 64], 'label': '51840.cr.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.c1.a1', '4.f1.b1', '4.g1.a1'], 'normal_contains': ['16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462277
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.e1.a1', '720.r1.a1', '1080.a1.a1'], 'contains': ['4320.f1.a1', '4320.h1.a1', '4320.i1.b1', '6480.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [8031, -1, 2455, -1, 3157, -1, 3152, -1], 'generators': [1, 8800, 2, 35840], 'label': '51840.cr.2160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '2160.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462278
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2160.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.e1.b1', '720.r1.a1', '1080.a1.a1'], 'contains': ['4320.f1.a1', '4320.h1.b1', '4320.i1.a1', '6480.o1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [8031, -1, 2981, -1, 3157, -1, 3426, -1], 'generators': [1, 8800, 2, 18240], 'label': '51840.cr.2160.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '2160.e1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2160.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462279
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '1296.a1.a1', '1296.b1.a1', '1296.c1.a1'], 'contains': ['5184.a1.a1', '5184.b1.a1', '5184.c1.a1', '12960.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4733, -1, 4214, -1, 5205, -1, 4173, -1], 'generators': [8640, 64, 160], 'label': '51840.cr.2592.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462280
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '1296.a1.a1', '1296.d1.a1'], 'contains': ['5184.a1.a1', '5184.d1.a1', '5184.e1.a1', '12960.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [5747, -1, 2593, -1, 4136, -1, 2282, -1], 'generators': [8640, 64, 2], 'label': '51840.cr.2592.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '2592.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462281
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '1296.a1.a1', '1296.e1.a1', '1296.f1.a1', '1296.g1.a1', '1296.g1.b1'], 'contains': ['5184.b1.a1', '5184.d1.a1', '12960.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4867, -1, 4304, -1, 5029, -1, 4328, -1], 'generators': [2, 64, 160], 'label': '51840.cr.2592.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462282
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '1296.a1.a1', '1296.h1.a1', '1296.i1.a1'], 'contains': ['5184.b1.a1', '5184.e1.a1', '12960.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5185, -1, 4367, -1, 5102, -1, 4264, -1], 'generators': [8642, 64, 160], 'label': '51840.cr.2592.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462283
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '1296.b1.a1', '1296.e1.a1', '1296.h1.a1', '1296.j1.a1', '1296.k1.a1', '1296.l1.a1', '1296.m1.a1'], 'contains': ['5184.b1.a1', '12960.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3137, -1, 6475, -1, 7050, -1, 6176, -1], 'generators': [80, 160, 64], 'label': '51840.cr.2592.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462284
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '1296.b1.a1', '1296.f1.a1', '1296.i1.a1'], 'contains': ['5184.b1.a1', '12960.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4163, -1, 5079, -1, 6084, -1, 4838, -1], 'generators': [8720, 160, 64], 'label': '51840.cr.2592.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462285
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '1296.c1.a1', '1296.e1.a1', '1296.i1.a1', '1296.n1.a1', '1296.n1.b1'], 'contains': ['5184.b1.a1', '12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2914, -1, 5693, -1, 6251, -1, 5413, -1], 'generators': [82, 64, 160], 'label': '51840.cr.2592.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462286
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '1296.c1.a1', '1296.f1.a1', '1296.h1.a1'], 'contains': ['5184.b1.a1', '12960.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3666, -1, 5228, -1, 5414, -1, 4904, -1], 'generators': [8722, 64, 160], 'label': '51840.cr.2592.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2592.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 223462287
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['6480.d1.a1', '6480.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.f1.a1', '4.g1.b1'], 'contains': ['16.h1.a1', '40.o1.b1', '648.o1.b1'], 'core': '8.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [556, 7729, 9478, 7262, 9037, 1764, 8737, 2090], 'generators': [17280, 23040, 200, 12800, 160, 960, 182, 80, 64], 'label': '51840.cr.8.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': ['4.c1.a1', '4.f1.a1', '4.g1.b1'], 'normal_contains': ['16.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462288
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '1296.a1.a1', '1296.o1.a1'], 'contains': ['5184.c1.a1', '5184.d1.a1', '5184.e1.a1', '12960.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6017, -1, 1648, -1, 4064, -1, 2347, -1], 'generators': [8800, 64, 2], 'label': '51840.cr.2592.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '2592.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462289
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '1296.d1.a1', '1296.g1.a1', '1296.o1.a1'], 'contains': ['5184.d1.a1', '12960.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [5949, -1, 2217, -1, 3967, -1, 2405, -1], 'generators': [1, 64, 2], 'label': '51840.cr.2592.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.b1.a1', 'old_label': '2592.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462290
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2592.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.b1', '1296.d1.a1', '1296.g1.b1', '1296.o1.a1'], 'contains': ['5184.d1.a1', '12960.j1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [5949, -1, 2705, -1, 3967, -1, 2457, -1], 'generators': [8641, 64, 2], 'label': '51840.cr.2592.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.b1.a1', 'old_label': '2592.j1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.j1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462291
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1.a1', '1440.a1.a1', '1440.c1.a1', '1440.c2.a1'], 'contains': ['5760.a1.a1', '8640.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [7900, -1, 1754, -1, 1306, -1, 817, -1], 'generators': [8640, 8000, 18240], 'label': '51840.cr.2880.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.d1.a1', 'old_label': '2880.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462292
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.a2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '160.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1.a1', '1440.a2.a1', '1440.b1.a1', '1440.d1.a1'], 'contains': ['5760.a2.a1', '8640.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7670, -1, 1996, -1, 2153, -1, 1080, -1], 'generators': [8640, 8000, 6720], 'label': '51840.cr.2880.a2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '2880.a2.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.a2.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462293
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.a3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1.a1', '1440.a3.a1'], 'contains': ['5760.a3.a1', '8640.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7146, -1, 2373, -1, 2508, -1, 1178, -1], 'generators': [8640, 8000, 41280], 'label': '51840.cr.2880.a3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.f1.a1', 'old_label': '2880.a3.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.a3.a1', 'subgroup_fusion': None, 'weyl_group': '8.1'}
  • id: 223462294
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.b1.a1', '1440.a1.a1', '1440.e1.a1', '1440.g1.a1'], 'contains': ['5760.a1.a1', '8640.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [7801, -1, 1835, -1, 1452, -1, 1601, -1], 'generators': [160, 8000, 18240], 'label': '51840.cr.2880.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '2880.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462295
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.b2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.b1.a1', '1440.a2.a1', '1440.f1.a1', '1440.h1.a1', '1440.i1.a1', '1440.j1.a1', '1440.k1.a1', '1440.l1.a1'], 'contains': ['5760.a2.a1', '8640.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6436, -1, 3067, -1, 3007, -1, 2516, -1], 'generators': [160, 8000, 6720], 'label': '51840.cr.2880.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '2880.b2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.b2.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462296
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.b3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.b1.a1', '1440.a3.a1', '1440.k2.a1', '1440.l2.a1'], 'contains': ['5760.a3.a1', '8640.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6345, -1, 3759, -1, 3081, -1, 2582, -1], 'generators': [160, 8000, 41280], 'label': '51840.cr.2880.b3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '2880.b3.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.b3.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462297
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.c1.a1', '1440.a1.a1', '1440.n1.a1', '1440.n2.a1'], 'contains': ['5760.a1.a1', '8640.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [8666, -1, 848, -1, 993, -1, 1438, -1], 'generators': [8800, 8000, 18240], 'label': '51840.cr.2880.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '720.a1.a1', 'old_label': '2880.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 223462298
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.m1.a1', '16.m1.b1', '16.o1.a1', '40.d1.a1', '648.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6161, -1, 2942, -1, 3473, -1, 3072, -1], 'generators': [17280, 23040, 8640, 8000, 2, 41280, 1, 160, 64], 'label': '51840.cr.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.j1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6480.bm'}
  • id: 223462299
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.c2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12960.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.c1.a1', '1440.a2.a1', '1440.m1.a1', '1440.o1.a1'], 'contains': ['5760.a2.a1', '8640.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8401, -1, 1236, -1, 2001, -1, 1667, -1], 'generators': [8800, 8000, 6720], 'label': '51840.cr.2880.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '2880.c2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.c2.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462300
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.c3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.c1.a1', '1440.a3.a1'], 'contains': ['5760.a3.a1', '8640.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8266, -1, 2238, -1, 2415, -1, 1733, -1], 'generators': [8800, 8000, 41280], 'label': '51840.cr.2880.c3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.f1.a1', 'old_label': '2880.c3.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.c3.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
  • id: 223462301
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.d1.a1', '1440.b1.a1', '1440.f1.a1', '1440.m1.a1', '1440.p1.a1', '1440.p1.b1'], 'contains': ['5760.a2.a1', '8640.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [8562, -1, 1493, -1, 2323, -1, 2189, -1], 'generators': [2, 2240, 18240], 'label': '51840.cr.2880.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '2880.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462302
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.d1.a1', '960.e1.a1', '1440.c1.a1', '1440.e1.a1', '1440.n1.a1'], 'contains': ['5760.a1.a1', '8640.d1.a1', '8640.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [9260, -1, 465, -1, 1085, -1, 1356, -1], 'generators': [2, 18240, 8000], 'label': '51840.cr.2880.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '2880.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462303
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.d1.a1', '960.e1.a1', '1440.c2.a1', '1440.e1.a1', '1440.n2.a1'], 'contains': ['5760.a1.a1', '8640.d1.a1', '8640.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [9048, -1, 579, -1, 1195, -1, 1520, -1], 'generators': [2, 24000, 8000], 'label': '51840.cr.2880.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '2880.e2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.e2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462304
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.e1.a1', '1440.d1.a1', '1440.f1.a1', '1440.o1.a1', '1440.q1.a1', '1440.q1.b1'], 'contains': ['5760.a2.a1', '8640.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8828, -1, 1002, -1, 1927, -1, 1904, -1], 'generators': [2, 8000, 6720], 'label': '51840.cr.2880.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '2880.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.f1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462305
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.f1.a1', '1440.b1.a1', '1440.h1.a1', '1440.o1.a1'], 'contains': ['5760.a2.a1', '8640.f1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [9384, -1, 686, -1, 1642, -1, 982, -1], 'generators': [8642, 2240, 18240], 'label': '51840.cr.2880.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '2880.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462306
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.f1.a1', '960.g1.a1', '1440.c1.a1', '1440.g1.a1', '1440.n2.a1'], 'contains': ['5760.a1.a1', '8640.f1.a1', '8640.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [9837, -1, 42, -1, 723, -1, 561, -1], 'generators': [8642, 18240, 8000], 'label': '51840.cr.2880.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '2880.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462307
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.h2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2880.a2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.f1.a1', '960.g1.a1', '1440.c2.a1', '1440.g1.a1', '1440.n1.a1'], 'contains': ['5760.a1.a1', '8640.f1.a1', '8640.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 240, 'diagramx': [9955, -1, 288, -1, 833, -1, 659, -1], 'generators': [8642, 24000, 8000], 'label': '51840.cr.2880.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '240.a1.a1', 'old_label': '2880.h2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.h2.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 223462308
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2880.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1440.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.g1.a1', '1440.d1.a1', '1440.h1.a1', '1440.m1.a1'], 'contains': ['5760.a2.a1', '8640.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9482, -1, 1172, -1, 1735, -1, 899, -1], 'generators': [8642, 8000, 6720], 'label': '51840.cr.2880.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '2880.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 223462309
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1'], 'contains': ['16.c1.a1', '16.n1.a1', '16.n1.b1', '40.f1.a1', '648.e1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1965, -1, 6632, -1, 6110, -1, 5625, -1], 'generators': [17280, 5760, 8640, 25280, 160, 35520, 21, 82, 64], 'label': '51840.cr.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '8.k1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462310
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '648.a1.a1', '1620.a1.a1', '1620.b1.a1', '1620.c1.a1'], 'contains': ['6480.a1.a1', '6480.b1.a1', '6480.c1.a1', '6480.e1.a1', '6480.f1.a1', '6480.h1.a1', '6480.i1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [3545, -1, 5948, -1, 6494, -1, 5664, -1], 'generators': [8640, 2, 80], 'label': '51840.cr.3240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462311
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.a1', '648.b1.a1', '1080.a1.a1', '1620.a1.a1'], 'contains': ['6480.a1.a1', '6480.d1.a1', '6480.g1.a1', '6480.g1.b1', '6480.o1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [5623, -1, 4639, -1, 3780, -1, 3994, -1], 'generators': [1, 8640, 160], 'label': '51840.cr.3240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.a1.a1', 'old_label': '3240.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462312
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.d1.a1', '648.c1.a1', '1620.b1.a1', '1620.d1.a1', '1620.e1.a1'], 'contains': ['6480.b1.a1', '6480.j1.a1', '6480.k1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [904, -1, 8751, -1, 8604, -1, 8260, -1], 'generators': [8640, 40], 'label': '51840.cr.3240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '3240.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462313
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.e1.a1', '648.d1.a1', '1620.b1.a1'], 'contains': ['6480.b1.a1', '6480.l1.a1', '6480.m1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2518, -1, 7514, -1, 8322, -1, 7792, -1], 'generators': [8640, 42], 'label': '51840.cr.3240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462314
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.f1.a1', '648.e1.a1', '1620.c1.a1'], 'contains': ['6480.c1.a1', '6480.n1.a1', '6480.n1.b1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [1514, -1, 6864, -1, 6928, -1, 6860, -1], 'generators': [21, 8640], 'label': '51840.cr.3240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.c1.a1', 'old_label': '3240.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462315
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.g1.a1', '360.h1.a1', '648.f1.a1', '1620.a1.a1', '1620.f1.a1', '1620.g1.a1'], 'contains': ['6480.e1.a1', '6480.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [4081, -1, 6069, -1, 5980, -1, 6027, -1], 'generators': [1, 80], 'label': '51840.cr.3240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.a1.a1', 'old_label': '3240.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462316
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.g1.b1', '360.h1.b1', '648.f1.b1', '1620.a1.a1', '1620.f1.b1', '1620.g1.a1'], 'contains': ['6480.e1.a1', '6480.g1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [4081, -1, 6160, -1, 5980, -1, 6093, -1], 'generators': [8641, 80], 'label': '51840.cr.3240.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.a1.a1', 'old_label': '3240.f1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462317
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.i1.a1', '648.g1.a1', '1620.b1.a1', '1620.f1.a1', '1620.f1.b1', '1620.h1.a1', '1620.h1.b1', '1620.i1.a1', '1620.i1.b1'], 'contains': ['6480.e1.a1', '6480.j1.a1', '6480.m1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2044, -1, 8360, -1, 8857, -1, 8143, -1], 'generators': [2, 40], 'label': '51840.cr.3240.g1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462318
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.j1.a1', '648.h1.a1', '1620.b1.a1', '1620.g1.a1', '1620.j1.a1'], 'contains': ['6480.e1.a1', '6480.k1.a1', '6480.l1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2636, -1, 7381, -1, 8069, -1, 7561, -1], 'generators': [8680, 2], 'label': '51840.cr.3240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462319
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.j1.a1', '648.i1.a1', '1620.c1.a1', '1620.h1.a1', '1620.j1.a1'], 'contains': ['6480.e1.a1', '6480.n1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [1011, -1, 7075, -1, 7942, -1, 7163, -1], 'generators': [21, 80], 'label': '51840.cr.3240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.b1.a1', 'old_label': '3240.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462320
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.d1.a1', '16.m1.a1', '40.g1.a1', '648.f1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4113, -1, 5582, -1, 5320, -1, 5222, -1], 'generators': [17280, 23040, 80, 8000, 160, 41280, 1, 2, 64], 'label': '51840.cr.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462321
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.j1.b1', '648.i1.b1', '1620.c1.a1', '1620.h1.b1', '1620.j1.a1'], 'contains': ['6480.e1.a1', '6480.n1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [1011, -1, 7210, -1, 7942, -1, 7313, -1], 'generators': [8661, 80], 'label': '51840.cr.3240.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.b1.a1', 'old_label': '3240.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.i1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 223462322
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.k1.a1', '360.l1.a1', '648.j1.a1', '1620.a1.a1'], 'contains': ['6480.f1.a1', '6480.g1.a1', '6480.g1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [5047, -1, 4909, -1, 4794, -1, 4620, -1], 'generators': [1, 8720], 'label': '51840.cr.3240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.a1.a1', 'old_label': '3240.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462323
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.m1.a1', '648.k1.a1', '1620.b1.a1', '1620.k1.a1', '1620.k1.b1'], 'contains': ['6480.h1.a1', '6480.j1.a1', '6480.l1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2162, -1, 7820, -1, 8715, -1, 8376, -1], 'generators': [8642, 40], 'label': '51840.cr.3240.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462324
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.n1.a1', '648.l1.a1', '1620.b1.a1'], 'contains': ['6480.h1.a1', '6480.k1.a1', '6480.m1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [1927, -1, 7963, -1, 8180, -1, 7462, -1], 'generators': [8680, 42], 'label': '51840.cr.3240.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462325
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.n1.a1', '648.m1.a1', '1620.c1.a1'], 'contains': ['6480.i1.a1', '6480.n1.a1', '6480.n1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [2269, -1, 6722, -1, 7626, -1, 6633, -1], 'generators': [21, 8720], 'label': '51840.cr.3240.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.c1.a1', 'old_label': '3240.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462326
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '648.n1.a1', '1620.d1.a1', '1620.i1.a1', '1620.k1.a1'], 'contains': ['6480.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [403, -1, 9383, -1, 9782, -1, 9658, -1], 'generators': [20], 'label': '51840.cr.3240.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '3240.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462327
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.b1', '648.n1.b1', '1620.d1.a1', '1620.i1.b1', '1620.k1.b1'], 'contains': ['6480.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [403, -1, 9775, -1, 9782, -1, 9590, -1], 'generators': [8660], 'label': '51840.cr.3240.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '3240.n1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462328
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.o1.a1', '648.o1.a1', '1620.e1.a1', '1620.i1.b1', '1620.k1.a1'], 'contains': ['6480.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [30, -1, 9586, -1, 9636, -1, 9347, -1], 'generators': [8822], 'label': '51840.cr.3240.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462329
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '3240.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.o1.b1', '648.o1.b1', '1620.e1.a1', '1620.i1.a1', '1620.k1.b1'], 'contains': ['6480.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [30, -1, 9958, -1, 9636, -1, 9247, -1], 'generators': [182], 'label': '51840.cr.3240.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '3240.o1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3240.o1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462330
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.a1.a1', '1440.a2.a1', '1440.a3.a1', '2160.a1.a1'], 'contains': ['8640.a1.a1', '8640.b1.a1', '8640.c1.a1', '12960.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [6725, -1, 3537, -1, 2794, -1, 2062, -1], 'generators': [8640, 160, 8000], 'label': '51840.cr.4320.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462331
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.d1.a1', '16.m1.b1', '40.g1.b1', '648.f1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4113, -1, 5448, -1, 5320, -1, 5327, -1], 'generators': [17280, 23040, 80, 8000, 160, 41280, 8641, 2, 64], 'label': '51840.cr.8.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.l1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462332
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.b1.a1', '1440.c1.a1', '1440.c2.a1', '2160.a1.a1', '2160.b1.a1', '2160.c1.a1'], 'contains': ['8640.a1.a1', '8640.d1.a1', '8640.f1.a1', '12960.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [6855, -1, 2825, -1, 2619, -1, 1986, -1], 'generators': [8640, 2, 18240], 'label': '51840.cr.4320.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '4320.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462333
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.c1.a1', '1440.c2.a1', '1440.d1.a1', '2160.a1.a1'], 'contains': ['8640.a1.a1', '8640.e1.a1', '8640.g1.a1', '12960.b1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [7372, -1, 1463, -1, 1860, -1, 1281, -1], 'generators': [8640, 2, 8000], 'label': '51840.cr.4320.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '4320.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462334
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.e1.a1', '1440.f1.a1', '2160.a1.a1', '2160.d1.a1', '2160.d1.b1'], 'contains': ['8640.b1.a1', '8640.d1.a1', '8640.e1.a1', '12960.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7454, -1, 3362, -1, 2704, -1, 2642, -1], 'generators': [2, 160, 8000], 'label': '51840.cr.4320.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462335
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.g1.a1', '1440.h1.a1', '2160.a1.a1'], 'contains': ['8640.b1.a1', '8640.f1.a1', '8640.g1.a1', '12960.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [9170, -1, 2724, -1, 2068, -1, 1792, -1], 'generators': [8642, 160, 8000], 'label': '51840.cr.4320.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462336
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.m1.a1', '1440.n1.a1', '1440.n2.a1', '2160.a1.a1', '2160.e1.a1', '2160.e1.b1'], 'contains': ['8640.c1.a1', '8640.d1.a1', '8640.g1.a1', '12960.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [8246, -1, 2143, -1, 2238, -1, 2114, -1], 'generators': [8800, 2, 18240], 'label': '51840.cr.4320.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462337
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.n1.a1', '1440.n2.a1', '1440.o1.a1', '2160.a1.a1'], 'contains': ['8640.c1.a1', '8640.e1.a1', '8640.f1.a1', '12960.i1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [8635, -1, 1162, -1, 1802, -1, 1845, -1], 'generators': [8800, 2, 8000], 'label': '51840.cr.4320.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462338
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.h1.a1', '1440.p1.a1', '2160.b1.a1', '2160.d1.a1', '2160.e1.a1'], 'contains': ['8640.d1.a1', '12960.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7745, -1, 2458, -1, 2934, -1, 3016, -1], 'generators': [1, 35840, 2], 'label': '51840.cr.4320.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462339
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.h1.b1', '1440.p1.b1', '2160.b1.a1', '2160.d1.b1', '2160.e1.b1'], 'contains': ['8640.d1.a1', '12960.j1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7745, -1, 3803, -1, 2934, -1, 3426, -1], 'generators': [8641, 35840, 2], 'label': '51840.cr.4320.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '4320.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462340
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.i1.a1', '1440.p1.a1', '2160.c1.a1', '2160.d1.a1', '2160.e1.b1'], 'contains': ['8640.d1.a1', '12960.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8023, -1, 2611, -1, 2861, -1, 2951, -1], 'generators': [1, 2, 18240], 'label': '51840.cr.4320.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '4320.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462341
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4320.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2160.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['480.i1.b1', '1440.p1.b1', '2160.c1.a1', '2160.d1.b1', '2160.e1.a1'], 'contains': ['8640.d1.a1', '12960.j1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8023, -1, 3201, -1, 2861, -1, 3179, -1], 'generators': [8641, 2, 18240], 'label': '51840.cr.4320.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '4320.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4320.i1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462360
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.j1.b1', '1296.g1.b1', '2160.d1.b1', '3240.b1.a1', '3240.f1.b1', '3240.j1.a1'], 'contains': ['12960.c1.a1', '12960.j1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [5413, -1, 4761, -1, 3912, -1, 4064, -1], 'generators': [8641, 160], 'label': '51840.cr.6480.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.a1.a1', 'old_label': '6480.g1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462342
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], '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', '4.g1.a1', '4.g1.b1', '10.c1.a1', '162.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [852, 7037, 8959, 7572, 8999, 2962, 9176, 2381], 'generators': [24000, 17280, 34880, 8640, 160, 40, 64, 20, 2, 80, 5760], 'label': '51840.cr.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.b1.a1', '4.c1.a1', '4.f1.b1', '4.f1.a1', '4.g1.b1', '4.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462343
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.d1.a1', '16.n1.a1', '40.j1.a1', '648.i1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2257, -1, 6310, -1, 7475, -1, 5891, -1], 'generators': [17280, 5760, 80, 40640, 160, 29760, 21, 82, 64], 'label': '51840.cr.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462344
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5184.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '2592.a1.a1', '2592.b1.a1'], 'contains': ['10368.a1.a1', '25920.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5123, -1, 4057, -1, 4290, -1, 2231, -1], 'generators': [8640, 64], 'label': '51840.cr.5184.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '5184.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462345
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5184.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '2592.a1.a1', '2592.c1.a1', '2592.d1.a1', '2592.e1.a1', '2592.f1.a1', '2592.g1.a1', '2592.h1.a1'], 'contains': ['10368.a1.a1', '25920.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4508, -1, 4343, -1, 5261, -1, 4296, -1], 'generators': [160, 64], 'label': '51840.cr.5184.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '5184.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462346
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5184.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '2592.a1.a1', '2592.i1.a1'], 'contains': ['10368.a1.a1', '25920.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5510, -1, 3995, -1, 4218, -1, 2347, -1], 'generators': [8800, 64], 'label': '51840.cr.5184.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '5184.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462347
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5184.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '2592.b1.a1', '2592.c1.a1', '2592.i1.a1', '2592.j1.a1', '2592.j1.b1'], 'contains': ['10368.a1.a1', '25920.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [5778, -1, 1934, -1, 4064, -1, 2464, -1], 'generators': [2, 64], 'label': '51840.cr.5184.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '5184.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462348
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5184.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1.a1', '2592.b1.a1', '2592.d1.a1', '2592.i1.a1'], 'contains': ['10368.a1.a1', '25920.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [5942, -1, 1873, -1, 4122, -1, 2289, -1], 'generators': [8642, 64], 'label': '51840.cr.5184.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '5184.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 223462349
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5760.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1920.a1.a1', '2880.a1.a1', '2880.b1.a1', '2880.c1.a1', '2880.e1.a1', '2880.e2.a1', '2880.h1.a1', '2880.h2.a1'], 'contains': ['17280.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [9317, -1, 526, -1, 1085, -1, 1356, -1], 'generators': [8000, 18240], 'label': '51840.cr.5760.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '640.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.d1.a1', 'old_label': '5760.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5760.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462350
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5760.a2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '160.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1920.a1.a1', '2880.a2.a1', '2880.b2.a1', '2880.c2.a1', '2880.d1.a1', '2880.f1.a1', '2880.g1.a1', '2880.i1.a1'], 'contains': ['17280.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8824, -1, 1069, -1, 2001, -1, 1625, -1], 'generators': [8000, 6720], 'label': '51840.cr.5760.a2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '640.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '5760.a2.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5760.a2.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
  • id: 223462351
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '5760.a3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1920.a1.a1', '2880.a3.a1', '2880.b3.a1', '2880.c3.a1'], 'contains': ['17280.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8311, -1, 2065, -1, 2415, -1, 1737, -1], 'generators': [8000, 41280], 'label': '51840.cr.5760.a3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '640.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.f1.a1', 'old_label': '5760.a3.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5760.a3.a1', 'subgroup_fusion': None, 'weyl_group': '8.1'}
  • id: 223462352
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '2160.a1.a1', '3240.a1.a1', '3240.b1.a1'], 'contains': ['12960.a1.a1', '12960.b1.a1', '12960.c1.a1', '12960.d1.a1', '12960.i1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [5751, -1, 4236, -1, 4001, -1, 3887, -1], 'generators': [8640, 2, 160], 'label': '51840.cr.6480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462353
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.c1.a1', '1296.b1.a1', '3240.a1.a1', '3240.c1.a1', '3240.d1.a1'], 'contains': ['12960.a1.a1', '12960.e1.a1', '12960.f1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4127, -1, 6127, -1, 6817, -1, 5762, -1], 'generators': [8640, 80], 'label': '51840.cr.6480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '6480.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462354
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.d1.a1', '16.n1.b1', '40.j1.b1', '648.i1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2257, -1, 6973, -1, 7475, -1, 6255, -1], 'generators': [17280, 5760, 80, 40640, 160, 29760, 8661, 82, 64], 'label': '51840.cr.8.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.m1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462355
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.d1.a1', '720.d2.a1', '1296.c1.a1', '3240.a1.a1', '3240.e1.a1'], 'contains': ['12960.a1.a1', '12960.g1.a1', '12960.h1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [3691, -1, 5493, -1, 5383, -1, 5208, -1], 'generators': [8640, 82], 'label': '51840.cr.6480.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462356
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.f1.a1', '1296.d1.a1', '2160.b1.a1', '2160.c1.a1', '3240.b1.a1'], 'contains': ['12960.b1.a1', '12960.j1.a1', '12960.j1.b1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [6153, -1, 3887, -1, 3677, -1, 3262, -1], 'generators': [1, 8640], 'label': '51840.cr.6480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '6480.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462357
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.g1.a1', '1296.e1.a1', '3240.a1.a1', '3240.f1.a1', '3240.f1.b1', '3240.g1.a1', '3240.h1.a1', '3240.i1.a1', '3240.i1.b1'], 'contains': ['12960.c1.a1', '12960.e1.a1', '12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [3102, -1, 6758, -1, 6678, -1, 6094, -1], 'generators': [2, 80], 'label': '51840.cr.6480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462358
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.h1.a1', '1296.f1.a1', '3240.a1.a1', '3240.j1.a1'], 'contains': ['12960.c1.a1', '12960.f1.a1', '12960.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [4635, -1, 5024, -1, 5108, -1, 4697, -1], 'generators': [8720, 2], 'label': '51840.cr.6480.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462359
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.j1.a1', '1296.g1.a1', '2160.d1.a1', '3240.b1.a1', '3240.f1.a1', '3240.j1.a1'], 'contains': ['12960.c1.a1', '12960.j1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [5413, -1, 4562, -1, 3912, -1, 3966, -1], 'generators': [1, 160], 'label': '51840.cr.6480.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.a1.a1', 'old_label': '6480.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462361
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.k1.a1', '1296.h1.a1', '3240.a1.a1', '3240.k1.a1', '3240.l1.a1'], 'contains': ['12960.d1.a1', '12960.e1.a1', '12960.h1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [3391, -1, 6353, -1, 6523, -1, 5911, -1], 'generators': [8642, 80], 'label': '51840.cr.6480.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462362
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.l1.a1', '1296.i1.a1', '3240.a1.a1', '3240.m1.a1'], 'contains': ['12960.d1.a1', '12960.f1.a1', '12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [3954, -1, 5266, -1, 5525, -1, 5082, -1], 'generators': [8720, 82], 'label': '51840.cr.6480.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462363
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.m1.a1', '1296.j1.a1', '3240.c1.a1', '3240.g1.a1', '3240.k1.a1', '3240.n1.a1', '3240.n1.b1', '3240.o1.a1', '3240.o1.b1'], 'contains': ['12960.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1415, -1, 8836, -1, 8750, -1, 8417, -1], 'generators': [40], 'label': '51840.cr.6480.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '6480.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462364
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.n1.a1', '1296.k1.a1', '3240.c1.a1', '3240.h1.a1', '3240.l1.a1'], 'contains': ['12960.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1940, -1, 7497, -1, 8004, -1, 7429, -1], 'generators': [8680], 'label': '51840.cr.6480.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '6480.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462365
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.e1.a1', '16.m1.a1', '16.m1.b1', '40.k1.a1', '648.j1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5466, -1, 4059, -1, 4362, -1, 3876, -1], 'generators': [17280, 23040, 8720, 8000, 160, 41280, 1, 2, 64], 'label': '51840.cr.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6480.bm'}
  • id: 223462366
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.o1.a1', '1296.l1.a1', '3240.d1.a1', '3240.h1.a1', '3240.k1.a1'], 'contains': ['12960.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2673, -1, 7332, -1, 8095, -1, 7635, -1], 'generators': [8682], 'label': '51840.cr.6480.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.l1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462367
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1620.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.p1.a1', '1296.m1.a1', '3240.d1.a1', '3240.g1.a1', '3240.l1.a1'], 'contains': ['12960.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [2350, -1, 7670, -1, 8251, -1, 7495, -1], 'generators': [42], 'label': '51840.cr.6480.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '6480.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 223462368
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.q1.a1', '1296.n1.a1', '3240.e1.a1', '3240.i1.a1', '3240.m1.a1'], 'contains': ['12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [1067, -1, 6550, -1, 6931, -1, 6593, -1], 'generators': [21], 'label': '51840.cr.6480.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.c1.a1', 'old_label': '6480.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462369
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.q1.b1', '1296.n1.b1', '3240.e1.a1', '3240.i1.b1', '3240.m1.a1'], 'contains': ['12960.g1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1620, 'diagramx': [1067, -1, 6967, -1, 6931, -1, 6700, -1], 'generators': [8661], 'label': '51840.cr.6480.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1620.c1.a1', 'old_label': '6480.n1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.n1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462370
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '6480.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['720.s1.a1', '1296.o1.a1', '2160.e1.a1', '2160.e1.b1', '3240.b1.a1'], 'contains': ['12960.i1.a1', '12960.j1.a1', '12960.j1.b1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 3240, 'diagramx': [6425, -1, 2681, -1, 3566, -1, 3097, -1], 'generators': [1, 8800], 'label': '51840.cr.6480.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3240.b1.a1', 'old_label': '6480.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6480.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462371
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '80.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.a1.a1', '2880.a2.a1', '2880.a3.a1', '4320.a1.a1', '4320.b1.a1', '4320.c1.a1'], 'contains': ['17280.a1.a1', '25920.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7401, -1, 2414, -1, 2325, -1, 1681, -1], 'generators': [8640, 8000], 'label': '51840.cr.8640.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '8640.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462372
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.b1.a1', '2880.b2.a1', '2880.b3.a1', '4320.a1.a1', '4320.d1.a1', '4320.e1.a1'], 'contains': ['17280.a1.a1', '25920.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [7304, -1, 3252, -1, 2749, -1, 2062, -1], 'generators': [160, 8000], 'label': '51840.cr.8640.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '8640.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462373
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6480.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.c1.a1', '2880.c2.a1', '2880.c3.a1', '4320.a1.a1', '4320.f1.a1', '4320.g1.a1'], 'contains': ['17280.a1.a1', '25920.c1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [8114, -1, 1686, -1, 2238, -1, 1845, -1], 'generators': [8800, 8000], 'label': '51840.cr.8640.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '8640.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462374
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.d1.a1', '2880.e1.a1', '2880.e2.a1', '4320.b1.a1', '4320.d1.a1', '4320.f1.a1', '4320.h1.a1', '4320.h1.b1', '4320.i1.a1', '4320.i1.b1'], 'contains': ['17280.a1.a1', '25920.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [8204, -1, 2324, -1, 2549, -1, 2114, -1], 'generators': [2, 18240], 'label': '51840.cr.8640.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '8640.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462375
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.e1.a1', '2880.e2.a1', '2880.f1.a1', '4320.c1.a1', '4320.d1.a1', '4320.g1.a1'], 'contains': ['17280.a1.a1', '25920.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [8686, -1, 1229, -1, 1926, -1, 1792, -1], 'generators': [2, 8000], 'label': '51840.cr.8640.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '8640.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462376
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1'], 'contains': ['16.g1.a1', '16.n1.a1', '16.n1.b1', '40.n1.a1', '648.m1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1773, -1, 6474, -1, 6293, -1, 5463, -1], 'generators': [17280, 5760, 8720, 40640, 160, 29760, 21, 82, 64], 'label': '51840.cr.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '8.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462377
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.g1.a1', '2880.h1.a1', '2880.h2.a1', '4320.b1.a1', '4320.e1.a1', '4320.g1.a1'], 'contains': ['17280.a1.a1', '25920.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [9482, -1, 807, -1, 1803, -1, 1570, -1], 'generators': [8642, 18240], 'label': '51840.cr.8640.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '360.b1.a1', 'old_label': '8640.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462378
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '8640.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.h1.a1', '2880.h2.a1', '2880.i1.a1', '4320.c1.a1', '4320.e1.a1', '4320.f1.a1'], 'contains': ['17280.a1.a1', '25920.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [9253, -1, 1440, -1, 1863, -1, 1465, -1], 'generators': [8642, 8000], 'label': '51840.cr.8640.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1.a1', 'old_label': '8640.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8640.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 223462379
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10368.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '5184.a1.a1', '5184.b1.a1', '5184.c1.a1', '5184.d1.a1', '5184.e1.a1'], 'contains': ['51840.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5488, -1, 1904, -1, 4122, -1, 2292, -1], 'generators': [64], 'label': '51840.cr.10368.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '10368.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10368.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 223462380
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.a1.a1', '4320.a1.a1', '6480.a1.a1', '6480.b1.a1', '6480.c1.a1'], 'contains': ['25920.a1.a1', '25920.b1.a1', '25920.c1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4882, -1, 4410, -1, 5016, -1, 4074, -1], 'generators': [8640, 160], 'label': '51840.cr.12960.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '12960.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462381
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.b1.a1', '4320.b1.a1', '4320.c1.a1', '6480.a1.a1', '6480.d1.a1'], 'contains': ['25920.a1.a1', '25920.d1.a1', '25920.e1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [6181, -1, 3123, -1, 3715, -1, 2169, -1], 'generators': [8640, 2], 'label': '51840.cr.12960.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '12960.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462382
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.c1.a1', '4320.d1.a1', '6480.a1.a1', '6480.e1.a1', '6480.f1.a1', '6480.g1.a1', '6480.g1.b1'], 'contains': ['25920.b1.a1', '25920.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [5095, -1, 4353, -1, 4030, -1, 4133, -1], 'generators': [2, 160], 'label': '51840.cr.12960.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '12960.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462383
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.d1.a1', '4320.e1.a1', '6480.a1.a1', '6480.h1.a1', '6480.i1.a1'], 'contains': ['25920.b1.a1', '25920.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [5576, -1, 4182, -1, 4949, -1, 4015, -1], 'generators': [8642, 160], 'label': '51840.cr.12960.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '12960.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462384
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.i1.a1', '2592.e1.a1', '6480.b1.a1', '6480.e1.a1', '6480.h1.a1', '6480.j1.a1', '6480.k1.a1', '6480.l1.a1', '6480.m1.a1'], 'contains': ['25920.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3266, -1, 6819, -1, 6901, -1, 6135, -1], 'generators': [80], 'label': '51840.cr.12960.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '12960.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462385
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.j1.a1', '2592.f1.a1', '6480.b1.a1', '6480.f1.a1', '6480.i1.a1'], 'contains': ['25920.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4380, -1, 4976, -1, 5247, -1, 4716, -1], 'generators': [8720], 'label': '51840.cr.12960.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '160.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '12960.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462386
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.k1.a1', '1440.k2.a1', '2592.g1.a1', '6480.c1.a1', '6480.e1.a1', '6480.i1.a1', '6480.n1.a1', '6480.n1.b1'], 'contains': ['25920.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [3037, -1, 5493, -1, 5454, -1, 5271, -1], 'generators': [82], 'label': '51840.cr.12960.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '12960.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462387
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.c1.a1', '20.f1.a1', '20.f1.b1', '20.g1.a1', '90.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3278, -1, 7159, -1, 5962, -1, 7152, -1], 'generators': [1, 40320, 80, 160, 17280, 8640, 2, 6720, 1280, 40], 'label': '51840.cr.10.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462388
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.l1.a1', '1440.l2.a1', '2592.h1.a1', '6480.c1.a1', '6480.f1.a1', '6480.h1.a1'], 'contains': ['25920.b1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 405, 'diagramx': [4232, -1, 5151, -1, 5109, -1, 4788, -1], 'generators': [8722], 'label': '51840.cr.12960.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '405.a1.a1', 'old_label': '12960.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462389
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '810.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2592.i1.a1', '4320.f1.a1', '4320.g1.a1', '6480.a1.a1', '6480.o1.a1'], 'contains': ['25920.c1.a1', '25920.d1.a1', '25920.e1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 810, 'diagramx': [7257, -1, 2235, -1, 3589, -1, 2408, -1], 'generators': [8800, 2], 'label': '51840.cr.12960.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '810.a1.a1', 'old_label': '12960.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462390
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.q1.a1', '2592.j1.a1', '4320.h1.a1', '4320.i1.a1', '6480.d1.a1', '6480.g1.a1', '6480.o1.a1'], 'contains': ['25920.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [6499, -1, 2607, -1, 3652, -1, 2983, -1], 'generators': [1], 'label': '51840.cr.12960.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '12960.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462391
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '12960.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1080.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1440.q1.b1', '2592.j1.b1', '4320.h1.b1', '4320.i1.b1', '6480.d1.a1', '6480.g1.b1', '6480.o1.a1'], 'contains': ['25920.d1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1080, 'diagramx': [6499, -1, 3007, -1, 3652, -1, 3138, -1], 'generators': [8641], 'label': '51840.cr.12960.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1080.a1.a1', 'old_label': '12960.j1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12960.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462392
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '17280.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '80.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5760.a1.a1', '5760.a2.a1', '5760.a3.a1', '8640.a1.a1', '8640.b1.a1', '8640.c1.a1', '8640.d1.a1', '8640.e1.a1', '8640.f1.a1', '8640.g1.a1'], 'contains': ['51840.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8628, -1, 1500, -1, 2238, -1, 1737, -1], 'generators': [8000], 'label': '51840.cr.17280.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '640.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '17280.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17280.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 223462393
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '25920.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['2.d1.a1', '2.d1.d1', '2.d1.b1', '2.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['5184.a1.a1', '8640.a1.a1', '12960.a1.a1', '12960.b1.a1'], 'contains': ['51840.a1.a1'], 'core': '25920.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5477, 2800, 4024, 1930, 3800, 6445, 2235, 6786], 'generators': [8640], 'label': '51840.cr.25920.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '25920.a1.a1', 'normal_contained_in': ['320.a1.a1'], 'normal_contains': ['51840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '25920.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': '1.1', 'quotient_action_kernel': '25920.dn', 'quotient_action_kernel_order': 25920, 'quotient_fusion': None, 'short_label': '25920.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462394
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '25920.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.b1.a1', '8640.b1.a1', '12960.a1.a1', '12960.c1.a1', '12960.d1.a1', '12960.e1.a1', '12960.f1.a1', '12960.g1.a1', '12960.h1.a1'], 'contains': ['51840.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4610, -1, 4446, -1, 5040, -1, 4198, -1], 'generators': [160], 'label': '51840.cr.25920.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '25920.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462395
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '25920.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.c1.a1', '8640.c1.a1', '12960.a1.a1', '12960.i1.a1'], 'contains': ['51840.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6480, -1, 2378, -1, 3742, -1, 2347, -1], 'generators': [8800], 'label': '51840.cr.25920.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '320.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '25920.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462396
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '25920.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.d1.a1', '8640.d1.a1', '8640.e1.a1', '12960.b1.a1', '12960.c1.a1', '12960.i1.a1', '12960.j1.a1', '12960.j1.b1'], 'contains': ['51840.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7159, -1, 2325, -1, 3683, -1, 2408, -1], 'generators': [2], 'label': '51840.cr.25920.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '25920.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462397
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '25920.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5184.e1.a1', '8640.f1.a1', '8640.g1.a1', '12960.b1.a1', '12960.d1.a1', '12960.i1.a1'], 'contains': ['51840.a1.a1'], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [7323, -1, 1850, -1, 3624, -1, 2183, -1], 'generators': [8642], 'label': '51840.cr.25920.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.a1.a1', 'old_label': '25920.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25920.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462398
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.d1.a1', '20.h1.a1', '20.h1.b1', '20.j1.a1', '810.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2428, -1, 7399, -1, 8208, -1, 7955, -1], 'generators': [21, 5760, 80, 160, 17280, 8640, 82, 29760, 40640, 40], 'label': '51840.cr.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462399
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '51840.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': ['10368.a1.a1', '17280.a1.a1', '25920.a1.a1', '25920.b1.a1', '25920.c1.a1', '25920.d1.a1', '25920.e1.a1'], 'contains': [], 'core': '51840.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6480, 2679, 2325, 2031, 3742, 6601, 2292, 6924], 'generators': [], 'label': '51840.cr.51840.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '51840.a1.a1', 'normal_contained_in': ['640.a1.a1', '25920.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '51840.a1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '51840.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 223462400
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.c1.a1', '20.e1.a1', '20.i1.a1', '20.i1.b1', '20.k1.a1', '20.k1.b1', '810.c1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1061, -1, 8832, -1, 8908, -1, 9095, -1], 'generators': [20, 5760, 80, 160, 17280, 8640, 40, 960, 46400, 2], 'label': '51840.cr.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462401
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '5.a1.a1'], 'contains': ['20.f1.a1', '20.h1.a1', '20.i1.a1', '810.d1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1501, -1, 8022, -1, 8527, -1, 8265, -1], 'generators': [1, 23040, 80, 160, 17280, 20, 40, 6720, 1280, 2], 'label': '51840.cr.10.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462402
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '5.a1.a1'], 'contains': ['20.f1.a1', '20.h1.b1', '20.i1.b1', '810.d1.b1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1501, -1, 8383, -1, 8527, -1, 8634, -1], 'generators': [1, 23040, 80, 160, 17280, 8660, 40, 6720, 1280, 2], 'label': '51840.cr.10.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462403
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.c1', '5.a1.a1'], 'contains': ['20.f1.b1', '20.h1.a1', '20.i1.b1', '810.d1.c1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1501, -1, 8142, -1, 8527, -1, 8511, -1], 'generators': [8641, 23040, 80, 160, 17280, 8660, 40, 6720, 1280, 2], 'label': '51840.cr.10.d1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.c1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.c1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462404
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['25920.a1.a1', '25920.c1.a1', '25920.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '10.d1.a1', '162.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1533, 4662, 8038, 4594, 8646, 5530, 8119, 3192], 'generators': [41280, 17280, 8000, 20, 160, 40, 64, 1, 2, 80, 23040], 'label': '51840.cr.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462405
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '10.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.d1', '5.a1.a1'], 'contains': ['20.f1.b1', '20.h1.b1', '20.i1.a1', '810.d1.d1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1501, -1, 8263, -1, 8527, -1, 8388, -1], 'generators': [8641, 23040, 80, 160, 17280, 20, 40, 6720, 1280, 2], 'label': '51840.cr.10.d1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.d1.d1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.d1.d1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462406
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.h1.a1', '32.i1.a1', '80.d1.a1', '1296.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5972, 1157, 2318, 1180, 3619, 9597, 2171, 8809], 'generators': [8640, 11840, 5760, 160, 41280, 17280, 2, 64], 'label': '51840.cr.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462407
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '80.a1.a1', '1296.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5022, 4538, 4698, 4418, 5740, 4401, 4848, 5542], 'generators': [8640, 11840, 23040, 64, 6720, 17280, 80, 160], 'label': '51840.cr.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '32.d1.a1', '32.e1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462408
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.k1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.g1.a1', '80.e1.a1', '1296.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4295, 2111, 4977, 381, 5079, 8690, 4490, 9616], 'generators': [8640, 29120, 23040, 160, 960, 17280, 82, 64], 'label': '51840.cr.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '32.f1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462409
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.m1.b1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.f1.a1', '80.g1.a1', '1296.e1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4467, 3708, 5559, 3105, 5583, 7173, 5429, 6244], 'generators': [2, 11840, 5760, 160, 41280, 17280, 80, 64], 'label': '51840.cr.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.a1.a1', '8.e1.a1', '8.d1.a1'], 'normal_contains': ['32.b1.a1', '32.d1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462410
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.n1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '32.g1.a1', '80.h1.a1', '1296.f1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5376, 327, 4163, 2489, 4362, 6474, 4054, 7488], 'generators': [8720, 12800, 23040, 160, 35520, 17280, 2, 64], 'label': '51840.cr.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.b1.a1', '32.e1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462411
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.g1.a1', '80.j1.a1', '1296.h1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4763, 5983, 4835, 3722, 5443, 5775, 4987, 6866], 'generators': [8642, 11840, 5760, 160, 41280, 17280, 80, 64], 'label': '51840.cr.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.a1.a1', '8.g1.a1', '8.f1.a1'], 'normal_contains': ['32.c1.a1', '32.d1.a1', '32.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462412
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.o1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.f1.a1', '80.k1.a1', '1296.i1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4616, 2972, 4534, 1876, 5242, 7872, 4345, 8106], 'generators': [8720, 12800, 5760, 160, 35520, 17280, 82, 64], 'label': '51840.cr.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.a1', '32.e1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462413
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.h1.a1', '8.h1.b1', '8.i1.a1', '8.i1.b1'], 'contains': ['32.d1.a1', '80.b1.a1', '1296.j1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2725, 7871, 8052, 7118, 8292, 2516, 8261, 3345], 'generators': [40, 8000, 5760, 80, 6720, 17280, 64, 160], 'label': '51840.cr.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.a1', '8.f1.a1', '8.h1.b1', '8.h1.a1', '8.i1.a1', '8.i1.b1'], 'normal_contains': ['32.d1.a1', '80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462414
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.e1.a1', '8.g1.a1'], 'contains': ['32.d1.a1', '80.c1.a1', '1296.k1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3058, 7268, 5976, 6091, 6779, 3089, 6609, 3854], 'generators': [8680, 8000, 5760, 80, 6720, 17280, 64, 160], 'label': '51840.cr.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.b1.a1', '8.e1.a1', '8.g1.a1'], 'normal_contains': ['32.d1.a1', '80.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462415
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['25920.a1.a1', '25920.c1.a1', '25920.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.b1', '4.f1.b1', '10.d1.b1', '162.d1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1533, 4662, 8493, 6768, 8646, 5530, 8733, 3923], 'generators': [41280, 17280, 8000, 8660, 160, 40, 64, 1, 2, 80, 23040], 'label': '51840.cr.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.b1', '4.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '51840.cr', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462416
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.d1.a1', '80.l1.a1', '1296.l1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3800, 6658, 5876, 5063, 6895, 3669, 6978, 4371], 'generators': [8682, 25280, 23040, 160, 960, 17280, 80, 64], 'label': '51840.cr.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.c1.a1', '8.e1.a1', '8.f1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462417
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1'], 'contains': ['32.d1.a1', '80.m1.a1', '1296.m1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3644, 5308, 6169, 5579, 7165, 5133, 6875, 4891], 'generators': [42, 25280, 23040, 160, 960, 17280, 80, 64], 'label': '51840.cr.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.c1.a1', '8.d1.a1', '8.g1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462418
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1'], 'contains': ['32.h1.a1', '32.j1.a1', '32.j1.b1', '80.f1.a1', '1296.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6473, -1, 2609, -1, 3319, -1, 1630, -1], 'generators': [1, 8000, 23040, 2, 41280, 17280, 8640, 64], 'label': '51840.cr.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1.a1', 'old_label': '16.l1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '3240.be'}
  • id: 223462419
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.l1.a1', '8.n1.a1'], 'contains': ['32.b1.a1', '32.j1.a1', '80.i1.a1', '1296.g1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6161, -1, 2858, -1, 3473, -1, 2997, -1], 'generators': [1, 8000, 23040, 2, 41280, 17280, 160, 64], 'label': '51840.cr.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.m1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6480.bm'}
  • id: 223462420
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.l1.b1', '8.n1.a1'], 'contains': ['32.b1.a1', '32.j1.b1', '80.i1.b1', '1296.g1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6161, -1, 3167, -1, 3473, -1, 3745, -1], 'generators': [8641, 8000, 23040, 2, 41280, 17280, 160, 64], 'label': '51840.cr.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.m1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6480.bm'}
  • id: 223462421
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.m1.a1', '8.o1.a1'], 'contains': ['32.f1.a1', '80.n1.a1', '1296.n1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1906, -1, 6270, -1, 6268, -1, 5571, -1], 'generators': [21, 25280, 5760, 160, 35520, 17280, 82, 64], 'label': '51840.cr.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.n1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462422
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.m1.b1', '8.o1.a1'], 'contains': ['32.f1.a1', '80.n1.b1', '1296.n1.b1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1906, -1, 6532, -1, 6268, -1, 5955, -1], 'generators': [8661, 25280, 5760, 160, 35520, 17280, 82, 64], 'label': '51840.cr.16.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.n1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 223462423
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1'], 'contains': ['32.i1.a1', '32.j1.a1', '32.j1.b1', '80.o1.a1', '1296.o1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6841, -1, 2996, -1, 3184, -1, 1510, -1], 'generators': [1, 8000, 23040, 2, 41280, 17280, 8800, 64], 'label': '51840.cr.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1.a1', 'old_label': '16.o1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '3240.be'}
  • id: 223462424
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['2592.j1.a1', '2592.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.b1.b1', '1620.d1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1481, 9673, 8595, 8253, 9194, 403, 9671, 369], 'generators': [20, 17280, 160, 46400, 8640, 80, 40320, 960, 40], 'label': '51840.cr.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['40.a1.a1', '40.b1.b1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': '20.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462425
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '10.a1.a1'], 'contains': ['40.c1.a1', '40.d1.a1', '40.g1.a1', '40.g1.b1', '40.k1.a1', '180.a1.a1', '180.b1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4541, -1, 5223, -1, 4838, -1, 5090, -1], 'generators': [1, 17280, 160, 1280, 8640, 2, 40320, 6720, 80], 'label': '51840.cr.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.lt'}
  • id: 223462426
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['25920.a1.a1', '25920.c1.a1', '25920.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.b1', '4.e1.a1', '4.f1.b1', '10.d1.c1', '162.d1.c1'], 'core': '2.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1533, 4662, 8181, 5319, 8646, 5530, 8588, 5385], 'generators': [41280, 17280, 8000, 8660, 160, 40, 64, 8641, 2, 80, 23040], 'label': '51840.cr.2.d1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.b1', '4.e1.a1', '4.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.c1', 'projective_image': '51840.cr', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.c1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462427
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '40.c1.a1', '40.e1.a1', '40.h1.a1', '40.i1.a1', '40.l1.a1', '40.m1.a1', '180.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3565, -1, 7233, -1, 7207, -1, 7379, -1], 'generators': [8640, 17280, 160, 8000, 2, 80, 5760, 6720, 40], 'label': '51840.cr.20.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462428
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '10.b1.a1'], 'contains': ['40.c1.a1', '40.f1.a1', '40.j1.a1', '40.j1.b1', '40.n1.a1', '1620.c1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2250, -1, 6473, -1, 6498, -1, 6073, -1], 'generators': [21, 17280, 160, 34880, 8640, 82, 5760, 47040, 80], 'label': '51840.cr.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.ct'}
  • id: 223462429
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '40.o1.a1', '40.o1.b1', '1620.e1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [919, -1, 8916, -1, 8718, -1, 9021, -1], 'generators': [182, 17280, 160, 25280, 8640, 80, 40320, 29760, 200], 'label': '51840.cr.20.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462430
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.a1.a1', '10.d1.a1', '10.d1.b1'], 'contains': ['40.g1.a1', '40.h1.a1', '180.d1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2991, -1, 7536, -1, 5962, -1, 7126, -1], 'generators': [1, 17280, 160, 1280, 40, 80, 40320, 6720, 2], 'label': '51840.cr.20.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462431
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '10.a1.a1', '10.d1.c1', '10.d1.d1'], 'contains': ['40.g1.b1', '40.h1.a1', '180.d1.b1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2991, -1, 7435, -1, 5962, -1, 7229, -1], 'generators': [8641, 17280, 160, 1280, 40, 80, 40320, 6720, 2], 'label': '51840.cr.20.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.f1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462432
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '10.a1.a1'], 'contains': ['40.g1.a1', '40.g1.b1', '40.i1.a1', '180.e1.a1', '180.e1.b1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4029, -1, 5545, -1, 5814, -1, 5755, -1], 'generators': [1, 17280, 160, 1280, 8680, 80, 40320, 6720, 2], 'label': '51840.cr.20.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.lt'}
  • id: 223462433
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.b1.a1', '10.d1.a1', '10.d1.c1'], 'contains': ['40.h1.a1', '40.j1.a1', '1620.h1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2699, -1, 7777, -1, 8505, -1, 7789, -1], 'generators': [21, 17280, 160, 40640, 40, 80, 5760, 29760, 82], 'label': '51840.cr.20.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.h1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462434
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '10.b1.a1', '10.d1.b1', '10.d1.d1'], 'contains': ['40.h1.a1', '40.j1.b1', '1620.h1.b1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2699, -1, 7940, -1, 8505, -1, 7955, -1], 'generators': [8661, 17280, 160, 40640, 40, 80, 5760, 29760, 82], 'label': '51840.cr.20.h1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.h1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462435
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.c1.a1', '10.d1.a1', '10.d1.d1'], 'contains': ['40.b1.a1', '40.h1.a1', '40.o1.b1', '1620.i1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1097, -1, 8280, -1, 8886, -1, 8576, -1], 'generators': [20, 17280, 160, 46400, 2, 80, 5760, 960, 40], 'label': '51840.cr.20.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.i1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462436
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '10.c1.a1', '10.d1.b1', '10.d1.c1'], 'contains': ['40.b1.b1', '40.h1.a1', '40.o1.a1', '1620.i1.b1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1097, -1, 8742, -1, 8886, -1, 8871, -1], 'generators': [8660, 17280, 160, 46400, 2, 80, 5760, 960, 40], 'label': '51840.cr.20.i1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.i1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.i1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462437
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['25920.a1.a1', '25920.c1.a1', '25920.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.b1', '4.e1.b1', '4.f1.a1', '10.d1.d1', '162.d1.d1'], 'core': '2.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1533, 4662, 8350, 6043, 8646, 5530, 8265, 4654], 'generators': [41280, 17280, 8000, 20, 160, 40, 64, 8641, 2, 80, 23040], 'label': '51840.cr.2.d1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.b1', '4.e1.b1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.d1', 'projective_image': '51840.cr', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.d1.d1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462438
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '10.b1.a1'], 'contains': ['40.i1.a1', '40.j1.a1', '40.j1.b1', '1620.j1.a1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2500, -1, 6651, -1, 7662, -1, 6422, -1], 'generators': [21, 17280, 160, 40640, 8680, 80, 5760, 29760, 82], 'label': '51840.cr.20.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2592.ct'}
  • id: 223462439
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '10.c1.a1'], 'contains': ['40.b1.a1', '40.l1.a1', '40.o1.a1', '1620.k1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1269, -1, 8449, -1, 9363, -1, 9521, -1], 'generators': [20, 17280, 160, 46400, 8642, 80, 5760, 960, 40], 'label': '51840.cr.20.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.k1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.k1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462440
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '20.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '10.c1.a1'], 'contains': ['40.b1.b1', '40.l1.a1', '40.o1.b1', '1620.k1.b1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 5, 'diagramx': [1269, -1, 9090, -1, 9363, -1, 9226, -1], 'generators': [182, 17280, 160, 25280, 8642, 80, 40320, 29760, 200], 'label': '51840.cr.20.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.k1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.k1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462441
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '160.a1.a1', '2592.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5730, 1678, 2768, 1180, 3966, 8690, 1743, 8809], 'generators': [8640, 40320, 64, 8000, 160, 17280, 12480], 'label': '51840.cr.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462442
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '16.m1.a1', '16.m1.b1'], 'contains': ['64.b1.a1', '64.d1.a1', '160.e1.a1', '2592.c1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6038, 912, 2542, 3437, 3545, 6760, 2864, 6532], 'generators': [2, 5760, 64, 11840, 160, 17280, 41280], 'label': '51840.cr.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462443
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.b1.a1', '64.e1.a1', '160.f1.a1', '2592.d1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5884, 4370, 2642, 2933, 3821, 7962, 2171, 7041], 'generators': [8642, 5760, 64, 11840, 160, 17280, 41280], 'label': '51840.cr.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.f1.a1', '16.g1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462444
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1'], 'contains': ['64.b1.a1', '160.b1.a1', '2592.e1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4805, 5308, 4893, 4727, 6202, 4986, 5396, 5513], 'generators': [80, 23040, 160, 11840, 64, 17280, 6720], 'label': '51840.cr.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.b1.a1', '16.d1.a1', '16.f1.a1', '16.i1.a1', '16.h1.a1', '16.j1.a1', '16.k1.a1'], 'normal_contains': ['64.b1.a1', '160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462445
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.e1.a1', '16.g1.a1'], 'contains': ['64.b1.a1', '160.c1.a1', '2592.f1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5389, 3106, 4163, 3942, 4541, 5558, 3876, 6022], 'generators': [8720, 23040, 160, 11840, 64, 17280, 6720], 'label': '51840.cr.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.b1.a1', '16.e1.a1', '16.g1.a1'], 'normal_contains': ['64.b1.a1', '160.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462446
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.d1.a1', '16.g1.a1', '16.n1.a1', '16.n1.b1'], 'contains': ['64.b1.a1', '160.g1.a1', '2592.g1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3418, 3738, 4997, 1847, 5928, 7361, 4705, 7575], 'generators': [82, 23040, 64, 29120, 160, 17280, 960], 'label': '51840.cr.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.c1.a1', '16.d1.a1', '16.g1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462447
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.e1.a1', '16.f1.a1'], 'contains': ['64.b1.a1', '160.h1.a1', '2592.h1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5229, 2473, 4501, 2403, 4209, 6159, 4208, 8135], 'generators': [8722, 23040, 64, 29120, 160, 17280, 960], 'label': '51840.cr.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.c1.a1', '16.e1.a1', '16.f1.a1'], 'normal_contains': ['64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462448
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '20.c1.a1', '324.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3102, 5583, 7356, 3047, 7641, 4618, 7634, 6990], 'generators': [5760, 41280, 2, 64, 80, 11840, 8640, 40, 160, 17280], 'label': '51840.cr.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', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.d1.a1', '8.g1.a1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462449
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.e1.a1', '160.d1.a1', '2592.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6473, -1, 1842, -1, 3319, -1, 441, -1], 'generators': [8640, 5760, 64, 11840, 2, 17280, 41280], 'label': '51840.cr.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462450
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.o1.a1'], 'contains': ['64.c1.a1', '64.d1.a1', '64.e1.a1', '160.i1.a1', '2592.i1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6651, -1, 1147, -1, 3185, -1, 559, -1], 'generators': [8800, 23040, 64, 29120, 2, 17280, 24000], 'label': '51840.cr.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.i1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12960.bx'}
  • id: 223462451
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.m1.a1', '16.o1.a1'], 'contains': ['64.d1.a1', '160.j1.a1', '2592.j1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6857, -1, 2426, -1, 2921, -1, 1516, -1], 'generators': [1, 23040, 64, 8000, 2, 17280, 41280], 'label': '51840.cr.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1.a1', 'old_label': '32.j1.a1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '3240.be'}
  • id: 223462452
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.m1.b1', '16.o1.a1'], 'contains': ['64.d1.a1', '160.j1.b1', '2592.j1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6857, -1, 3059, -1, 2921, -1, 1625, -1], 'generators': [8641, 23040, 64, 8000, 2, 17280, 41280], 'label': '51840.cr.32.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.j1.a1', 'old_label': '32.j1.b1', 'projective_image': '51840.cr', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.b1', 'subgroup_fusion': None, 'weyl_group': '3240.be'}
  • id: 223462453
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.a1.a1', '20.c1.a1', '20.e1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '80.c1.a1', '360.d1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2721, 8357, 7558, 6566, 7526, 1846, 7801, 2748], 'generators': [8640, 8000, 6720, 40, 160, 17280, 5760, 80], 'label': '51840.cr.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.b1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '80.c1.a1', '80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462454
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['1296.d1.a1', '1296.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '20.a1.a1', '20.i1.a1', '20.k1.a1'], 'contains': ['80.b1.a1', '3240.n1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1282, 9127, 8419, 8282, 8896, 1130, 8885, 1526], 'generators': [20, 46400, 960, 40, 160, 17280, 40320, 80], 'label': '51840.cr.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.h1.a1', '20.a1.a1'], 'normal_contains': ['80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '51840.cr', 'quotient_action_image': '20.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462455
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': ['1296.d1.a1', '1296.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '20.a1.a1', '20.i1.b1', '20.k1.b1'], 'contains': ['80.b1.a1', '3240.n1.b1'], 'core': '40.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1282, 9127, 8905, 7777, 8896, 1130, 8784, 1017], 'generators': [8660, 46400, 960, 40, 160, 17280, 40320, 80], 'label': '51840.cr.40.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.b1', 'normal_contained_in': ['8.h1.b1', '20.a1.a1'], 'normal_contains': ['80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.b1', 'projective_image': '51840.cr', 'quotient_action_image': '20.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '40.b1.b1', 'subgroup_fusion': None, 'weyl_group': '25920.dn'}
  • id: 223462456
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1'], 'contains': ['80.a1.a1', '80.d1.a1', '80.e1.a1', '80.g1.a1', '80.h1.a1', '80.j1.a1', '80.k1.a1', '360.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5014, -1, 4611, -1, 4695, -1, 4671, -1], 'generators': [8640, 8000, 6720, 2, 160, 17280, 5760, 80], 'label': '51840.cr.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}
  • id: 223462457
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '20.b1.a1'], 'contains': ['80.d1.a1', '80.f1.a1', '80.i1.a1', '80.i1.b1', '80.o1.a1', '120.a1.a1', '360.b1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7057, -1, 2759, -1, 2724, -1, 3147, -1], 'generators': [1, 1280, 6720, 8640, 2, 17280, 40320, 160], 'label': '51840.cr.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.d1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3499'}
  • id: 223462458
    {'ambient': '51840.cr', 'aut_centralizer_order': None, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '25920.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '80.l1.a1', '80.m1.a1', '360.e1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3918, -1, 5846, -1, 7031, -1, 6727, -1], 'generators': [8640, 8000, 6720, 42, 160, 17280, 5760, 80], 'label': '51840.cr.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '40.e1.a1', 'projective_image': '25920.dn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.ce'}