Abstract group data - 4752.h

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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': '72.18', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [30, 60, 30, 30, 30, 20, 60], 'aut_gens': [[20085218158, 3378821867, 158006], [5631369956, 1063703468, 43033609], [6569931495, 3441392746, 61408357], [11137597909, 21524346294, 49040219], [8071630041, 4442525157, 53148375], [688278810, 20585784533, 45940046], [8196771472, 20398072121, 52666417], [19709793673, 23902035630, 51939113]], 'aut_group': None, 'aut_hash': 8446468809167927362, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 63360, 'aut_permdeg': 140, 'aut_perms': [2796989794723060621287333003814897861881898028899043760989458456674387656048001923767892020704778643462930741518682557721325487772730808879832654963884084241042536524305987922717538466042249485193356295395118936320171642643885132043362343736, 11243351564314250459052369544593217242993430295366276471171037439311271126080610278101932006743339904155389571721520975877897358270161984140054868926373604010832612010219006342128802731089911631626319728714244316490405876757973027742194558448, 10341163202951751848766892108932230393231722891699212535532269285618710079836180509917766716045207700313350025173675159273706739581849898482495827200988603132622849214033772429789252312404199722958059698308236342764500527784961760244313652254, 13241632587907499504188964141646694333691239459878441133675300024602810313836693614687269296004502671047096252044049189924848800212937889669593981673281872097128522459282232070228370607391540541846062180259639663431167331184002769201649348006, 4785294253833984377805475080250001306113725209249609811413747752853797455027498125405366129719050462926862728099468748727734351155612563509510453372692584198639843917388764369461260982155797360877920957875512217198858180047286436175574909677, 2389408163975657385310478389261234214964510907671964248189496692934836824682140361051802934706024477991132493195439612107817770832014672674964454220944585186248941961285347572543073339434098706374310322440286633857089019866396281596534842209, 1385187938858170914316133128620910960918639686949933272607290087691777613768570971836159380652749667200404622996333991717300020663689108665644785218973554421142026852650702644082303046109054344721422570613085243303357756359285476944671109241], 'aut_phi_ratio': 44.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 66, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 66, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 66, 4, 1], [9, 1, 6, 1], [9, 2, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 66, 4, 1], [18, 1, 6, 1], [18, 2, 6, 2], [18, 2, 12, 1], [18, 66, 12, 1], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 2], [33, 2, 20, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 12, 2], [36, 66, 12, 1], [44, 2, 10, 2], [66, 2, 10, 2], [66, 2, 20, 3], [66, 2, 40, 1], [99, 2, 30, 1], [99, 2, 60, 1], [132, 2, 20, 4], [132, 2, 40, 2], [198, 2, 30, 1], [198, 2, 60, 2], [198, 2, 120, 1], [396, 2, 60, 2], [396, 2, 120, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{66}.C_{30}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '1320.142', 'autcentquo_hash': 142, 'autcentquo_nilpotent': False, 'autcentquo_order': 1320, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 66, 2], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 2, 1], [4, 66, 2], [6, 1, 2], [6, 2, 11], [6, 66, 4], [9, 1, 6], [9, 2, 6], [11, 2, 5], [12, 1, 4], [12, 2, 14], [12, 66, 4], [18, 1, 6], [18, 2, 24], [18, 66, 12], [22, 2, 15], [33, 2, 40], [36, 1, 12], [36, 2, 30], [36, 66, 12], [44, 2, 20], [66, 2, 120], [99, 2, 90], [132, 2, 160], [198, 2, 270], [396, 2, 360]], 'center_label': '36.2', 'center_order': 36, 'central_product': True, 'central_quotient': '132.9', 'commutator_count': 1, 'commutator_label': '66.4', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['528.149', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 66, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 66, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 66, 2, 2], [9, 1, 6, 1], [9, 2, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 66, 2, 2], [18, 1, 6, 1], [18, 2, 6, 4], [18, 66, 6, 2], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 2], [33, 2, 20, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 12, 2], [36, 66, 6, 2], [44, 2, 10, 2], [66, 2, 10, 2], [66, 2, 20, 5], [99, 2, 30, 1], [99, 2, 60, 1], [132, 2, 20, 4], [132, 2, 40, 2], [198, 2, 30, 1], [198, 2, 60, 4], [396, 2, 60, 2], [396, 2, 120, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 471744, 'exponent': 396, 'exponents_of_order': [4, 3, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 240]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '792.134', 'hash': 3521362650719687116, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [22, 66, 2], 'inner_gens': [[20085218158, 3378821867, 60098257], [20085218158, 3378821867, 22434867], [1564269646, 7821346679, 158006]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 132, 'inner_split': True, 'inner_tex': 'D_{66}', 'inner_used': [1, 2, 3], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': None, 'irrep_stats': [[1, 72], [2, 1170]], 'label': '4752.h', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D132:C18', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 66, 'number_characteristic_subgroups': 81, 'number_conjugacy_classes': 1242, 'number_divisions': 76, 'number_normal_subgroups': 105, 'number_subgroup_autclasses': 208, 'number_subgroup_classes': 272, 'number_subgroups': 2320, 'old_label': None, 'order': 4752, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 135], [3, 8], [4, 136], [6, 288], [9, 18], [11, 10], [12, 296], [18, 846], [22, 30], [33, 80], [36, 864], [44, 40], [66, 240], [99, 180], [132, 320], [198, 540], [396, 720]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 2, 30], 'outer_gen_pows': [62570774, 62570774, 62570774, 62570774, 5819082193], 'outer_gens': [[23276327632, 7320780743, 158006], [23276327632, 17019250599, 158006], [23276327632, 17519816535, 158006], [7946488521, 3378821867, 158006], [23401469218, 4379954490, 52666417]], 'outer_group': '480.1213', 'outer_hash': 1213, 'outer_nilpotent': True, 'outer_order': 480, 'outer_permdeg': 18, 'outer_perms': [40279680, 355687428096000, 1307674368000, 362880, 6227026593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 31, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 5], [6, 8], [8, 4], [10, 4], [12, 4], [20, 8], [24, 3], [40, 5], [60, 4], [80, 4], [120, 4], [240, 3]], 'representations': {'PC': {'code': '95912109259417760139608623166727838487080807171684600119001', 'gens': [1, 2, 6], 'pres': [8, -2, -2, -3, -3, -11, -2, -2, -3, 41505, 41, 962, 90, 3843, 123, 14404, 209093, 141, 221766, 166, 202759]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [20085218158, 3378821867, 158006]}, 'Perm': {'d': 31, 'gens': [265895334133363481073122580104280, 18598592312775672096228942937705, 558294921665220406931422093113387]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 18], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{132}:C_{18}', 'transitive_degree': 792, '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: 107718770
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 8, 'group_order': 4752, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 62570774, 'size': 1}
  • id: 107719124
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 8, 'group_order': 4752, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 24778026504, 'size': 1}
  • id: 107719235
    {'aut_label': '2B', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 8, 'group_order': 4752, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 62571169, 'size': 2}
  • id: 107719346
    {'aut_label': '2C', 'centralizer': '66.f1.a1', 'counter': 4, 'group_counter': 8, 'group_order': 4752, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 57710302, 'size': 66}
  • id: 107719457
    {'aut_label': '2C', 'centralizer': '66.f1.b1', 'counter': 5, 'group_counter': 8, 'group_order': 4752, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 34174157, 'size': 66}
  • id: 107719568
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 8, 'group_order': 4752, 'label': '3A1', 'order': 3, 'powers': [7, 1, 7, 7], 'representative': 2127406316, 'size': 1}
  • id: 107719679
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 8, 'group_order': 4752, 'label': '3A-1', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 22650620188, 'size': 1}
  • id: 107719790
    {'aut_label': '3B', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 8, 'group_order': 4752, 'label': '3B', 'order': 3, 'powers': [8, 1, 8, 8], 'representative': 2127406644, 'size': 2}
  • id: 107719901
    {'aut_label': '3C1', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 8, 'group_order': 4752, 'label': '3C1', 'order': 3, 'powers': [10, 1, 10, 10], 'representative': 22650619827, 'size': 2}
  • id: 107718771
    {'aut_label': '3C1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 8, 'group_order': 4752, 'label': '3C-1', 'order': 3, 'powers': [9, 1, 9, 9], 'representative': 2127406283, 'size': 2}
  • id: 107718882
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 8, 'group_order': 4752, 'label': '4A1', 'order': 4, 'powers': [2, 12, 11, 12], 'representative': 20898638516, 'size': 1}
  • id: 107718993
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 8, 'group_order': 4752, 'label': '4A-1', 'order': 4, 'powers': [2, 11, 12, 11], 'representative': 3941958762, 'size': 1}
  • id: 107719047
    {'aut_label': '4B', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 8, 'group_order': 4752, 'label': '4B', 'order': 4, 'powers': [2, 13, 13, 13], 'representative': 3941959033, 'size': 2}
  • id: 107719058
    {'aut_label': '4C', 'centralizer': '66.f1.b1', 'counter': 14, 'group_counter': 8, 'group_order': 4752, 'label': '4C', 'order': 4, 'powers': [2, 14, 14, 14], 'representative': 16782381, 'size': 66}
  • id: 107719069
    {'aut_label': '4C', 'centralizer': '66.f1.a1', 'counter': 15, 'group_counter': 8, 'group_order': 4752, 'label': '4D', 'order': 4, 'powers': [2, 15, 15, 15], 'representative': 31521006, 'size': 66}
  • id: 107719080
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 8, 'group_order': 4752, 'label': '6A1', 'order': 6, 'powers': [7, 2, 17, 17], 'representative': 22713190962, 'size': 1}
  • id: 107719091
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 8, 'group_order': 4752, 'label': '6A-1', 'order': 6, 'powers': [6, 2, 16, 16], 'representative': 2189977090, 'size': 1}
  • id: 107719102
    {'aut_label': '6B', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 8, 'group_order': 4752, 'label': '6B', 'order': 6, 'powers': [8, 2, 18, 18], 'representative': 2189977418, 'size': 2}
  • id: 107719113
    {'aut_label': '6C1', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 8, 'group_order': 4752, 'label': '6C1', 'order': 6, 'powers': [9, 3, 20, 20], 'representative': 2127406678, 'size': 2}
  • id: 107719125
    {'aut_label': '6C1', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 8, 'group_order': 4752, 'label': '6C-1', 'order': 6, 'powers': [10, 3, 19, 19], 'representative': 22650620222, 'size': 2}
  • id: 107719136
    {'aut_label': '6C1', 'centralizer': '2.b1.a1', 'counter': 21, 'group_counter': 8, 'group_order': 4752, 'label': '6D1', 'order': 6, 'powers': [9, 3, 22, 22], 'representative': 22713190600, 'size': 2}
  • id: 107719147
    {'aut_label': '6C1', 'centralizer': '2.b1.a1', 'counter': 22, 'group_counter': 8, 'group_order': 4752, 'label': '6D-1', 'order': 6, 'powers': [10, 3, 21, 21], 'representative': 2189977056, 'size': 2}
  • id: 107719158
    {'aut_label': '6E1', 'centralizer': '2.b1.a1', 'counter': 23, 'group_counter': 8, 'group_order': 4752, 'label': '6E1', 'order': 6, 'powers': [8, 3, 24, 24], 'representative': 22650620189, 'size': 2}
  • id: 107719169
    {'aut_label': '6E1', 'centralizer': '2.b1.a1', 'counter': 24, 'group_counter': 8, 'group_order': 4752, 'label': '6E-1', 'order': 6, 'powers': [8, 3, 23, 23], 'representative': 2127406317, 'size': 2}
  • id: 107719180
    {'aut_label': '6F1', 'centralizer': '2.b1.a1', 'counter': 25, 'group_counter': 8, 'group_order': 4752, 'label': '6F1', 'order': 6, 'powers': [9, 2, 26, 26], 'representative': 22713190995, 'size': 2}
  • id: 107719191
    {'aut_label': '6F1', 'centralizer': '2.b1.a1', 'counter': 26, 'group_counter': 8, 'group_order': 4752, 'label': '6F-1', 'order': 6, 'powers': [10, 2, 25, 25], 'representative': 2189977451, 'size': 2}
  • id: 107719202
    {'aut_label': '6G1', 'centralizer': '2.b1.a1', 'counter': 27, 'group_counter': 8, 'group_order': 4752, 'label': '6G1', 'order': 6, 'powers': [7, 3, 28, 28], 'representative': 2127406645, 'size': 2}
  • id: 107719213
    {'aut_label': '6G1', 'centralizer': '2.b1.a1', 'counter': 28, 'group_counter': 8, 'group_order': 4752, 'label': '6G-1', 'order': 6, 'powers': [6, 3, 27, 27], 'representative': 22650619861, 'size': 2}
  • id: 107719224
    {'aut_label': '6H1', 'centralizer': '66.f1.a1', 'counter': 29, 'group_counter': 8, 'group_order': 4752, 'label': '6H1', 'order': 6, 'powers': [6, 4, 30, 30], 'representative': 45920593, 'size': 66}
  • id: 107719236
    {'aut_label': '6H1', 'centralizer': '66.f1.a1', 'counter': 30, 'group_counter': 8, 'group_order': 4752, 'label': '6H-1', 'order': 6, 'powers': [7, 4, 29, 29], 'representative': 21668260, 'size': 66}
  • id: 107719247
    {'aut_label': '6H1', 'centralizer': '66.f1.b1', 'counter': 31, 'group_counter': 8, 'group_order': 4752, 'label': '6I1', 'order': 6, 'powers': [7, 5, 32, 32], 'representative': 31234372, 'size': 66}
  • id: 107719258
    {'aut_label': '6H1', 'centralizer': '66.f1.b1', 'counter': 32, 'group_counter': 8, 'group_order': 4752, 'label': '6I-1', 'order': 6, 'powers': [6, 5, 31, 31], 'representative': 60048235, 'size': 66}
  • id: 107719269
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 33, 'group_counter': 8, 'group_order': 4752, 'label': '9A1', 'order': 9, 'powers': [35, 6, 38, 35], 'representative': 19522081488, 'size': 1}
  • id: 107719280
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 34, 'group_counter': 8, 'group_order': 4752, 'label': '9A-1', 'order': 9, 'powers': [36, 7, 37, 36], 'representative': 875990836, 'size': 1}
  • id: 107719291
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 35, 'group_counter': 8, 'group_order': 4752, 'label': '9A2', 'order': 9, 'powers': [37, 7, 33, 37], 'representative': 4943091146, 'size': 1}
  • id: 107719302
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 36, 'group_counter': 8, 'group_order': 4752, 'label': '9A-2', 'order': 9, 'powers': [38, 6, 34, 38], 'representative': 12263871704, 'size': 1}
  • id: 107719313
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 37, 'group_counter': 8, 'group_order': 4752, 'label': '9A4', 'order': 9, 'powers': [34, 6, 35, 34], 'representative': 17895241364, 'size': 1}
  • id: 107719324
    {'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 38, 'group_counter': 8, 'group_order': 4752, 'label': '9A-4', 'order': 9, 'powers': [33, 7, 36, 33], 'representative': 19021515296, 'size': 1}
  • id: 107719335
    {'aut_label': '9B1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 8, 'group_order': 4752, 'label': '9B1', 'order': 9, 'powers': [41, 7, 44, 41], 'representative': 19021515071, 'size': 2}
  • id: 107719347
    {'aut_label': '9B1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 8, 'group_order': 4752, 'label': '9B-1', 'order': 9, 'powers': [42, 6, 43, 42], 'representative': 17895241274, 'size': 2}
  • id: 107719358
    {'aut_label': '9B1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 8, 'group_order': 4752, 'label': '9B2', 'order': 9, 'powers': [43, 6, 39, 43], 'representative': 19522081462, 'size': 2}
  • id: 107719369
    {'aut_label': '9B1', 'centralizer': '2.b1.a1', 'counter': 42, 'group_counter': 8, 'group_order': 4752, 'label': '9B-2', 'order': 9, 'powers': [44, 7, 40, 44], 'representative': 875991126, 'size': 2}
  • id: 107719380
    {'aut_label': '9B1', 'centralizer': '2.b1.a1', 'counter': 43, 'group_counter': 8, 'group_order': 4752, 'label': '9B4', 'order': 9, 'powers': [40, 7, 41, 40], 'representative': 4943091081, 'size': 2}
  • id: 107719391
    {'aut_label': '9B1', 'centralizer': '2.b1.a1', 'counter': 44, 'group_counter': 8, 'group_order': 4752, 'label': '9B-4', 'order': 9, 'powers': [39, 6, 42, 39], 'representative': 12263871820, 'size': 2}
  • id: 107719402
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 45, 'group_counter': 8, 'group_order': 4752, 'label': '11A1', 'order': 11, 'powers': [46, 47, 49, 1], 'representative': 10449319217, 'size': 2}
  • id: 107719413
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 46, 'group_counter': 8, 'group_order': 4752, 'label': '11A2', 'order': 11, 'powers': [48, 49, 45, 1], 'representative': 6194506920, 'size': 2}
  • id: 107719424
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 47, 'group_counter': 8, 'group_order': 4752, 'label': '11A3', 'order': 11, 'powers': [49, 46, 48, 1], 'representative': 16018118178, 'size': 2}
  • id: 107719435
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 48, 'group_counter': 8, 'group_order': 4752, 'label': '11A4', 'order': 11, 'powers': [47, 45, 46, 1], 'representative': 17081821045, 'size': 2}
  • id: 107719446
    {'aut_label': '11A1', 'centralizer': '2.b1.a1', 'counter': 49, 'group_counter': 8, 'group_order': 4752, 'label': '11A5', 'order': 11, 'powers': [45, 48, 47, 1], 'representative': 20836067440, 'size': 2}
  • id: 107719458
    {'aut_label': '12A1', 'centralizer': '1.a1.a1', 'counter': 50, 'group_counter': 8, 'group_order': 4752, 'label': '12A1', 'order': 12, 'powers': [16, 11, 52, 51], 'representative': 11075026998, 'size': 1}
  • id: 107719469
    {'aut_label': '12A1', 'centralizer': '1.a1.a1', 'counter': 51, 'group_counter': 8, 'group_order': 4752, 'label': '12A-1', 'order': 12, 'powers': [17, 12, 53, 50], 'representative': 15016985760, 'size': 1}
  • id: 107719480
    {'aut_label': '12A1', 'centralizer': '1.a1.a1', 'counter': 52, 'group_counter': 8, 'group_order': 4752, 'label': '12A5', 'order': 12, 'powers': [17, 11, 50, 53], 'representative': 9823611518, 'size': 1}
  • id: 107719491
    {'aut_label': '12A1', 'centralizer': '1.a1.a1', 'counter': 53, 'group_counter': 8, 'group_order': 4752, 'label': '12A-5', 'order': 12, 'powers': [16, 12, 51, 52], 'representative': 13765570280, 'size': 1}
  • id: 107719502
    {'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 54, 'group_counter': 8, 'group_order': 4752, 'label': '12B1', 'order': 12, 'powers': [18, 13, 55, 54], 'representative': 15016985697, 'size': 2}
  • id: 107719513
    {'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 55, 'group_counter': 8, 'group_order': 4752, 'label': '12B5', 'order': 12, 'powers': [18, 13, 54, 55], 'representative': 13765570217, 'size': 2}
  • id: 107719524
    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 56, 'group_counter': 8, 'group_order': 4752, 'label': '12C1', 'order': 12, 'powers': [18, 11, 56, 57], 'representative': 9823611538, 'size': 2}
  • id: 107719535
    {'aut_label': '12C1', 'centralizer': '2.b1.a1', 'counter': 57, 'group_counter': 8, 'group_order': 4752, 'label': '12C-1', 'order': 12, 'powers': [18, 12, 57, 56], 'representative': 13765570300, 'size': 2}
  • id: 107719546
    {'aut_label': '12D1', 'centralizer': '2.b1.a1', 'counter': 58, 'group_counter': 8, 'group_order': 4752, 'label': '12D1', 'order': 12, 'powers': [16, 13, 59, 59], 'representative': 13765570237, 'size': 2}
  • id: 107719557
    {'aut_label': '12D1', 'centralizer': '2.b1.a1', 'counter': 59, 'group_counter': 8, 'group_order': 4752, 'label': '12D-1', 'order': 12, 'powers': [17, 13, 58, 58], 'representative': 9823611601, 'size': 2}
  • id: 107719569
    {'aut_label': '12E1', 'centralizer': '2.b1.a1', 'counter': 60, 'group_counter': 8, 'group_order': 4752, 'label': '12E1', 'order': 12, 'powers': [25, 13, 62, 61], 'representative': 13765570123, 'size': 2}
  • id: 107719580
    {'aut_label': '12E1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 8, 'group_order': 4752, 'label': '12E-1', 'order': 12, 'powers': [26, 13, 63, 60], 'representative': 9823611695, 'size': 2}
  • id: 107719591
    {'aut_label': '12E1', 'centralizer': '2.b1.a1', 'counter': 62, 'group_counter': 8, 'group_order': 4752, 'label': '12E5', 'order': 12, 'powers': [26, 13, 60, 63], 'representative': 15016985583, 'size': 2}
  • id: 107719602
    {'aut_label': '12E1', 'centralizer': '2.b1.a1', 'counter': 63, 'group_counter': 8, 'group_order': 4752, 'label': '12E-5', 'order': 12, 'powers': [25, 13, 61, 62], 'representative': 11075027155, 'size': 2}
  • id: 107719613
    {'aut_label': '12F1', 'centralizer': '2.b1.a1', 'counter': 64, 'group_counter': 8, 'group_order': 4752, 'label': '12F1', 'order': 12, 'powers': [26, 11, 66, 65], 'representative': 9823611424, 'size': 2}
  • id: 107719624
    {'aut_label': '12F1', 'centralizer': '2.b1.a1', 'counter': 65, 'group_counter': 8, 'group_order': 4752, 'label': '12F-1', 'order': 12, 'powers': [25, 12, 67, 64], 'representative': 13765570394, 'size': 2}
  • id: 107719635
    {'aut_label': '12F1', 'centralizer': '2.b1.a1', 'counter': 66, 'group_counter': 8, 'group_order': 4752, 'label': '12F5', 'order': 12, 'powers': [25, 11, 64, 67], 'representative': 11075026884, 'size': 2}
  • id: 107719646
    {'aut_label': '12F1', 'centralizer': '2.b1.a1', 'counter': 67, 'group_counter': 8, 'group_order': 4752, 'label': '12F-5', 'order': 12, 'powers': [26, 12, 65, 66], 'representative': 15016985854, 'size': 2}
  • id: 107719657
    {'aut_label': '12G1', 'centralizer': '66.f1.b1', 'counter': 68, 'group_counter': 8, 'group_order': 4752, 'label': '12G1', 'order': 12, 'powers': [16, 14, 69, 69], 'representative': 21724634, 'size': 66}
  • id: 107719668
    {'aut_label': '12G1', 'centralizer': '66.f1.b1', 'counter': 69, 'group_counter': 8, 'group_order': 4752, 'label': '12G-1', 'order': 12, 'powers': [17, 14, 68, 68], 'representative': 4942253, 'size': 66}
  • id: 107719680
    {'aut_label': '12G1', 'centralizer': '66.f1.a1', 'counter': 70, 'group_counter': 8, 'group_order': 4752, 'label': '12H1', 'order': 12, 'powers': [17, 15, 71, 71], 'representative': 59918416, 'size': 66}
  • id: 107719691
    {'aut_label': '12G1', 'centralizer': '66.f1.a1', 'counter': 71, 'group_counter': 8, 'group_order': 4752, 'label': '12H-1', 'order': 12, 'powers': [16, 15, 70, 70], 'representative': 28555019, 'size': 66}
  • id: 107719702
    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 72, 'group_counter': 8, 'group_order': 4752, 'label': '18A1', 'order': 18, 'powers': [34, 16, 74, 77], 'representative': 6945355914, 'size': 1}
  • id: 107719713
    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 73, 'group_counter': 8, 'group_order': 4752, 'label': '18A-1', 'order': 18, 'powers': [33, 17, 75, 76], 'representative': 5819081982, 'size': 1}
  • id: 107719724
    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 74, 'group_counter': 8, 'group_order': 4752, 'label': '18A5', 'order': 18, 'powers': [37, 17, 76, 72], 'representative': 19897506132, 'size': 1}
  • id: 107719735
    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 75, 'group_counter': 8, 'group_order': 4752, 'label': '18A-5', 'order': 18, 'powers': [38, 16, 77, 73], 'representative': 12576725574, 'size': 1}
  • id: 107719746
    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 76, 'group_counter': 8, 'group_order': 4752, 'label': '18A7', 'order': 18, 'powers': [35, 16, 73, 74], 'representative': 5318515790, 'size': 1}
  • id: 107719757
    {'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 77, 'group_counter': 8, 'group_order': 4752, 'label': '18A-7', 'order': 18, 'powers': [36, 17, 72, 75], 'representative': 23964606442, 'size': 1}
  • id: 107719768
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 78, 'group_counter': 8, 'group_order': 4752, 'label': '18B1', 'order': 18, 'powers': [39, 27, 80, 83], 'representative': 12263871593, 'size': 2}
  • id: 107719779
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 79, 'group_counter': 8, 'group_order': 4752, 'label': '18B-1', 'order': 18, 'powers': [40, 28, 81, 82], 'representative': 4943091450, 'size': 2}
  • id: 107719791
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 80, 'group_counter': 8, 'group_order': 4752, 'label': '18B5', 'order': 18, 'powers': [44, 28, 82, 78], 'representative': 875990915, 'size': 2}
  • id: 107719802
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 81, 'group_counter': 8, 'group_order': 4752, 'label': '18B-5', 'order': 18, 'powers': [43, 27, 83, 79], 'representative': 19522081287, 'size': 2}
  • id: 107719813
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 82, 'group_counter': 8, 'group_order': 4752, 'label': '18B7', 'order': 18, 'powers': [42, 27, 79, 80], 'representative': 17895241279, 'size': 2}
  • id: 107719824
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 83, 'group_counter': 8, 'group_order': 4752, 'label': '18B-7', 'order': 18, 'powers': [41, 28, 78, 81], 'representative': 19021515310, 'size': 2}
  • id: 107719835
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 84, 'group_counter': 8, 'group_order': 4752, 'label': '18C1', 'order': 18, 'powers': [43, 27, 86, 89], 'representative': 17895241163, 'size': 2}
  • id: 107719846
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 85, 'group_counter': 8, 'group_order': 4752, 'label': '18C-1', 'order': 18, 'powers': [44, 28, 87, 88], 'representative': 19021515375, 'size': 2}
  • id: 107719857
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 86, 'group_counter': 8, 'group_order': 4752, 'label': '18C5', 'order': 18, 'powers': [41, 28, 88, 84], 'representative': 4943091160, 'size': 2}
  • id: 107719868
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 87, 'group_counter': 8, 'group_order': 4752, 'label': '18C-5', 'order': 18, 'powers': [42, 27, 89, 85], 'representative': 12263871619, 'size': 2}
  • id: 107719879
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 88, 'group_counter': 8, 'group_order': 4752, 'label': '18C7', 'order': 18, 'powers': [39, 27, 85, 86], 'representative': 19522081377, 'size': 2}
  • id: 107719890
    {'aut_label': '18B1', 'centralizer': '2.b1.a1', 'counter': 89, 'group_counter': 8, 'group_order': 4752, 'label': '18C-7', 'order': 18, 'powers': [40, 28, 84, 87], 'representative': 875991140, 'size': 2}
  • id: 107719902
    {'aut_label': '18D1', 'centralizer': '2.b1.a1', 'counter': 90, 'group_counter': 8, 'group_order': 4752, 'label': '18D1', 'order': 18, 'powers': [35, 27, 92, 95], 'representative': 19522081261, 'size': 2}
  • id: 107719913
    {'aut_label': '18D1', 'centralizer': '2.b1.a1', 'counter': 91, 'group_counter': 8, 'group_order': 4752, 'label': '18D-1', 'order': 18, 'powers': [36, 28, 93, 94], 'representative': 875991205, 'size': 2}
  • id: 107719924
    {'aut_label': '18D1', 'centralizer': '2.b1.a1', 'counter': 92, 'group_counter': 8, 'group_order': 4752, 'label': '18D5', 'order': 18, 'powers': [33, 28, 94, 90], 'representative': 19021515085, 'size': 2}
  • id: 107719935
    {'aut_label': '18D1', 'centralizer': '2.b1.a1', 'counter': 93, 'group_counter': 8, 'group_order': 4752, 'label': '18D-5', 'order': 18, 'powers': [34, 27, 95, 91], 'representative': 17895241189, 'size': 2}
  • id: 107719946
    {'aut_label': '18D1', 'centralizer': '2.b1.a1', 'counter': 94, 'group_counter': 8, 'group_order': 4752, 'label': '18D7', 'order': 18, 'powers': [38, 27, 91, 92], 'representative': 12263871709, 'size': 2}
  • id: 107719957
    {'aut_label': '18D1', 'centralizer': '2.b1.a1', 'counter': 95, 'group_counter': 8, 'group_order': 4752, 'label': '18D-7', 'order': 18, 'powers': [37, 28, 90, 93], 'representative': 4943091385, 'size': 2}
  • id: 107719968
    {'aut_label': '18E1', 'centralizer': '2.b1.a1', 'counter': 96, 'group_counter': 8, 'group_order': 4752, 'label': '18E1', 'order': 18, 'powers': [39, 16, 98, 101], 'representative': 12576725458, 'size': 2}
  • id: 107719979
    {'aut_label': '18E1', 'centralizer': '2.b1.a1', 'counter': 97, 'group_counter': 8, 'group_order': 4752, 'label': '18E-1', 'order': 18, 'powers': [40, 17, 99, 100], 'representative': 19897506197, 'size': 2}
  • id: 107719990
    {'aut_label': '18E1', 'centralizer': '2.b1.a1', 'counter': 98, 'group_counter': 8, 'group_order': 4752, 'label': '18E5', 'order': 18, 'powers': [44, 17, 100, 96], 'representative': 23964606152, 'size': 2}
  • id: 107720001
    {'aut_label': '18E1', 'centralizer': '2.b1.a1', 'counter': 99, 'group_counter': 8, 'group_order': 4752, 'label': '18E-5', 'order': 18, 'powers': [43, 16, 101, 97], 'representative': 5318515816, 'size': 2}
  • id: 107718772
    {'aut_label': '18E1', 'centralizer': '2.b1.a1', 'counter': 100, 'group_counter': 8, 'group_order': 4752, 'label': '18E7', 'order': 18, 'powers': [42, 16, 97, 98], 'representative': 6945356004, 'size': 2}
  • id: 107718783
    {'aut_label': '18E1', 'centralizer': '2.b1.a1', 'counter': 101, 'group_counter': 8, 'group_order': 4752, 'label': '18E-7', 'order': 18, 'powers': [41, 17, 96, 99], 'representative': 5819082207, 'size': 2}
  • id: 107718794
    {'aut_label': '18F1', 'centralizer': '66.f1.a1', 'counter': 102, 'group_counter': 8, 'group_order': 4752, 'label': '18F1', 'order': 18, 'powers': [33, 29, 104, 107], 'representative': 16392527, 'size': 66}
  • id: 107718805
    {'aut_label': '18F1', 'centralizer': '66.f1.a1', 'counter': 103, 'group_counter': 8, 'group_order': 4752, 'label': '18F-1', 'order': 18, 'powers': [34, 30, 105, 106], 'representative': 28057975, 'size': 66}
  • id: 107718816
    {'aut_label': '18F1', 'centralizer': '66.f1.a1', 'counter': 104, 'group_counter': 8, 'group_order': 4752, 'label': '18F5', 'order': 18, 'powers': [38, 30, 106, 102], 'representative': 19231871, 'size': 66}
  • id: 107718827
    {'aut_label': '18F1', 'centralizer': '66.f1.a1', 'counter': 105, 'group_counter': 8, 'group_order': 4752, 'label': '18F-5', 'order': 18, 'powers': [37, 29, 107, 103], 'representative': 56740431, 'size': 66}
  • id: 107718838
    {'aut_label': '18F1', 'centralizer': '66.f1.a1', 'counter': 106, 'group_counter': 8, 'group_order': 4752, 'label': '18F7', 'order': 18, 'powers': [36, 29, 103, 104], 'representative': 52012161, 'size': 66}
  • id: 107718849
    {'aut_label': '18F1', 'centralizer': '66.f1.a1', 'counter': 107, 'group_counter': 8, 'group_order': 4752, 'label': '18F-7', 'order': 18, 'powers': [35, 30, 102, 105], 'representative': 15291646, 'size': 66}
  • id: 107718860
    {'aut_label': '18F1', 'centralizer': '66.f1.b1', 'counter': 108, 'group_counter': 8, 'group_order': 4752, 'label': '18G1', 'order': 18, 'powers': [34, 31, 110, 113], 'representative': 37985754, 'size': 66}
  • id: 107718871
    {'aut_label': '18F1', 'centralizer': '66.f1.b1', 'counter': 109, 'group_counter': 8, 'group_order': 4752, 'label': '18G-1', 'order': 18, 'powers': [33, 32, 111, 112], 'representative': 8198050, 'size': 66}
  • id: 107718883
    {'aut_label': '18F1', 'centralizer': '66.f1.b1', 'counter': 110, 'group_counter': 8, 'group_order': 4752, 'label': '18G5', 'order': 18, 'powers': [37, 32, 112, 108], 'representative': 28372002, 'size': 66}
  • id: 107718894
    {'aut_label': '18F1', 'centralizer': '66.f1.b1', 'counter': 111, 'group_counter': 8, 'group_order': 4752, 'label': '18G-5', 'order': 18, 'powers': [38, 31, 113, 109], 'representative': 47127076, 'size': 66}
  • id: 107718905
    {'aut_label': '18F1', 'centralizer': '66.f1.b1', 'counter': 112, 'group_counter': 8, 'group_order': 4752, 'label': '18G7', 'order': 18, 'powers': [35, 31, 109, 110], 'representative': 40034671, 'size': 66}
  • id: 107718916
    {'aut_label': '18F1', 'centralizer': '66.f1.b1', 'counter': 113, 'group_counter': 8, 'group_order': 4752, 'label': '18G-7', 'order': 18, 'powers': [36, 32, 108, 111], 'representative': 26007867, 'size': 66}
  • id: 107718927
    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 114, 'group_counter': 8, 'group_order': 4752, 'label': '22A1', 'order': 22, 'powers': [48, 115, 116, 2], 'representative': 250283390, 'size': 2}
  • id: 107718938
    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 115, 'group_counter': 8, 'group_order': 4752, 'label': '22A3', 'order': 22, 'powers': [45, 118, 117, 2], 'representative': 4004529838, 'size': 2}
  • id: 107718949
    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 116, 'group_counter': 8, 'group_order': 4752, 'label': '22A5', 'order': 22, 'powers': [46, 117, 115, 2], 'representative': 14391278061, 'size': 2}
  • id: 107718960
    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 117, 'group_counter': 8, 'group_order': 4752, 'label': '22A7', 'order': 22, 'powers': [49, 114, 118, 2], 'representative': 6695072852, 'size': 2}
  • id: 107718971
    {'aut_label': '22A1', 'centralizer': '2.b1.a1', 'counter': 118, 'group_counter': 8, 'group_order': 4752, 'label': '22A9', 'order': 22, 'powers': [47, 116, 114, 2], 'representative': 7758776233, 'size': 2}
  • id: 107718982
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 119, 'group_counter': 8, 'group_order': 4752, 'label': '22B1', 'order': 22, 'powers': [45, 121, 123, 3], 'representative': 1939694027, 'size': 2}
  • id: 107718994
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 120, 'group_counter': 8, 'group_order': 4752, 'label': '22B-1', 'order': 22, 'powers': [45, 122, 124, 3], 'representative': 20836067775, 'size': 2}
  • id: 107719005
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 121, 'group_counter': 8, 'group_order': 4752, 'label': '22B3', 'order': 22, 'powers': [47, 127, 126, 3], 'representative': 1001132492, 'size': 2}
  • id: 107719016
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 122, 'group_counter': 8, 'group_order': 4752, 'label': '22B-3', 'order': 22, 'powers': [47, 128, 125, 3], 'representative': 17081821410, 'size': 2}
  • id: 107719027
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 123, 'group_counter': 8, 'group_order': 4752, 'label': '22B5', 'order': 22, 'powers': [49, 126, 121, 3], 'representative': 18145524311, 'size': 2}
  • id: 107719038
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 124, 'group_counter': 8, 'group_order': 4752, 'label': '22B-5', 'order': 22, 'powers': [49, 125, 122, 3], 'representative': 16018117995, 'size': 2}
  • id: 107719042
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 125, 'group_counter': 8, 'group_order': 4752, 'label': '22B7', 'order': 22, 'powers': [48, 120, 128, 3], 'representative': 24590314087, 'size': 2}
  • id: 107719043
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 126, 'group_counter': 8, 'group_order': 4752, 'label': '22B-7', 'order': 22, 'powers': [48, 119, 127, 3], 'representative': 6194506531, 'size': 2}
  • id: 107719044
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 127, 'group_counter': 8, 'group_order': 4752, 'label': '22B9', 'order': 22, 'powers': [46, 123, 119, 3], 'representative': 7883917628, 'size': 2}
  • id: 107719045
    {'aut_label': '22B1', 'centralizer': '2.b1.a1', 'counter': 128, 'group_counter': 8, 'group_order': 4752, 'label': '22B-9', 'order': 22, 'powers': [46, 124, 120, 3], 'representative': 10449319362, 'size': 2}
  • id: 107719046
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 129, 'group_counter': 8, 'group_order': 4752, 'label': '33A1', 'order': 33, 'powers': [130, 46, 132, 8], 'representative': 10699602515, 'size': 2}
  • id: 107719048
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 130, 'group_counter': 8, 'group_order': 4752, 'label': '33A2', 'order': 33, 'powers': [131, 48, 135, 8], 'representative': 16268401235, 'size': 2}
  • id: 107719049
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 131, 'group_counter': 8, 'group_order': 4752, 'label': '33A4', 'order': 33, 'powers': [134, 47, 136, 8], 'representative': 6882785344, 'size': 2}
  • id: 107719050
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 132, 'group_counter': 8, 'group_order': 4752, 'label': '33A5', 'order': 33, 'powers': [135, 45, 134, 8], 'representative': 9448186957, 'size': 2}
  • id: 107719051
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 133, 'group_counter': 8, 'group_order': 4752, 'label': '33A7', 'order': 33, 'powers': [137, 47, 130, 8], 'representative': 22150053762, 'size': 2}
  • id: 107719052
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 134, 'group_counter': 8, 'group_order': 4752, 'label': '33A8', 'order': 33, 'powers': [138, 49, 133, 8], 'representative': 11888447010, 'size': 2}
  • id: 107719053
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 135, 'group_counter': 8, 'group_order': 4752, 'label': '33A10', 'order': 33, 'powers': [136, 46, 138, 8], 'representative': 10762173323, 'size': 2}
  • id: 107719054
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 136, 'group_counter': 8, 'group_order': 4752, 'label': '33A13', 'order': 33, 'powers': [133, 48, 129, 8], 'representative': 6632502144, 'size': 2}
  • id: 107719055
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 137, 'group_counter': 8, 'group_order': 4752, 'label': '33A14', 'order': 33, 'powers': [132, 49, 131, 8], 'representative': 16330971861, 'size': 2}
  • id: 107719056
    {'aut_label': '33A1', 'centralizer': '2.b1.a1', 'counter': 138, 'group_counter': 8, 'group_order': 4752, 'label': '33A16', 'order': 33, 'powers': [129, 45, 137, 8], 'representative': 23151186157, 'size': 2}
  • id: 107719057
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 139, 'group_counter': 8, 'group_order': 4752, 'label': '33B1', 'order': 33, 'powers': [141, 46, 145, 7], 'representative': 22963474023, 'size': 2}
  • id: 107719059
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 140, 'group_counter': 8, 'group_order': 4752, 'label': '33B-1', 'order': 33, 'powers': [142, 46, 146, 6], 'representative': 10762173127, 'size': 2}
  • id: 107719060
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 141, 'group_counter': 8, 'group_order': 4752, 'label': '33B2', 'order': 33, 'powers': [143, 48, 139, 6], 'representative': 6632502193, 'size': 2}
  • id: 107719061
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 142, 'group_counter': 8, 'group_order': 4752, 'label': '33B-2', 'order': 33, 'powers': [144, 48, 140, 7], 'representative': 12889579498, 'size': 2}
  • id: 107719062
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 143, 'group_counter': 8, 'group_order': 4752, 'label': '33B4', 'order': 33, 'powers': [147, 47, 141, 7], 'representative': 7508493074, 'size': 2}
  • id: 107719063
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 144, 'group_counter': 8, 'group_order': 4752, 'label': '33B-4', 'order': 33, 'powers': [148, 47, 142, 6], 'representative': 22150053752, 'size': 2}
  • id: 107719064
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 145, 'group_counter': 8, 'group_order': 4752, 'label': '33B5', 'order': 33, 'powers': [139, 45, 148, 6], 'representative': 23151186244, 'size': 2}
  • id: 107719065
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 146, 'group_counter': 8, 'group_order': 4752, 'label': '33B-5', 'order': 33, 'powers': [140, 45, 147, 7], 'representative': 9197903782, 'size': 2}
  • id: 107719066
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 147, 'group_counter': 8, 'group_order': 4752, 'label': '33B8', 'order': 33, 'powers': [146, 49, 143, 6], 'representative': 6757643624, 'size': 2}
  • id: 107719067
    {'aut_label': '33B1', 'centralizer': '2.b1.a1', 'counter': 148, 'group_counter': 8, 'group_order': 4752, 'label': '33B-8', 'order': 33, 'powers': [145, 49, 144, 7], 'representative': 16330971943, 'size': 2}
  • id: 107719068
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 149, 'group_counter': 8, 'group_order': 4752, 'label': '33C1', 'order': 33, 'powers': [151, 45, 155, 9], 'representative': 9448186739, 'size': 2}
  • id: 107719070
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 150, 'group_counter': 8, 'group_order': 4752, 'label': '33C-1', 'order': 33, 'powers': [152, 45, 156, 10], 'representative': 14641561155, 'size': 2}
  • id: 107719071
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 151, 'group_counter': 8, 'group_order': 4752, 'label': '33C2', 'order': 33, 'powers': [153, 46, 161, 10], 'representative': 10762173212, 'size': 2}
  • id: 107719072
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 152, 'group_counter': 8, 'group_order': 4752, 'label': '33C-2', 'order': 33, 'powers': [154, 46, 162, 9], 'representative': 22963473981, 'size': 2}
  • id: 107719073
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 153, 'group_counter': 8, 'group_order': 4752, 'label': '33C4', 'order': 33, 'powers': [159, 48, 164, 9], 'representative': 12889579269, 'size': 2}
  • id: 107719074
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 154, 'group_counter': 8, 'group_order': 4752, 'label': '33C-4', 'order': 33, 'powers': [160, 48, 163, 10], 'representative': 6632502271, 'size': 2}
  • id: 107719075
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 155, 'group_counter': 8, 'group_order': 4752, 'label': '33C5', 'order': 33, 'powers': [161, 49, 160, 10], 'representative': 8759908319, 'size': 2}
  • id: 107719076
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 156, 'group_counter': 8, 'group_order': 4752, 'label': '33C-5', 'order': 33, 'powers': [162, 49, 159, 9], 'representative': 11888447263, 'size': 2}
  • id: 107719077
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 157, 'group_counter': 8, 'group_order': 4752, 'label': '33C7', 'order': 33, 'powers': [165, 48, 151, 9], 'representative': 16268401313, 'size': 2}
  • id: 107719078
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 158, 'group_counter': 8, 'group_order': 4752, 'label': '33C-7', 'order': 33, 'powers': [166, 48, 152, 10], 'representative': 15955547146, 'size': 2}
  • id: 107719079
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 159, 'group_counter': 8, 'group_order': 4752, 'label': '33C8', 'order': 33, 'powers': [167, 47, 157, 10], 'representative': 22150053809, 'size': 2}
  • id: 107719081
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 160, 'group_counter': 8, 'group_order': 4752, 'label': '33C-8', 'order': 33, 'powers': [168, 47, 158, 9], 'representative': 7508492886, 'size': 2}
  • id: 107719082
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 161, 'group_counter': 8, 'group_order': 4752, 'label': '33C10', 'order': 33, 'powers': [164, 45, 168, 9], 'representative': 9197903904, 'size': 2}
  • id: 107719083
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 162, 'group_counter': 8, 'group_order': 4752, 'label': '33C-10', 'order': 33, 'powers': [163, 45, 167, 10], 'representative': 23151186026, 'size': 2}
  • id: 107719084
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 163, 'group_counter': 8, 'group_order': 4752, 'label': '33C13', 'order': 33, 'powers': [158, 46, 150, 9], 'representative': 20773496892, 'size': 2}
  • id: 107719085
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 164, 'group_counter': 8, 'group_order': 4752, 'label': '33C-13', 'order': 33, 'powers': [157, 46, 149, 10], 'representative': 10699602473, 'size': 2}
  • id: 107719086
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 165, 'group_counter': 8, 'group_order': 4752, 'label': '33C14', 'order': 33, 'powers': [156, 47, 153, 10], 'representative': 6882785156, 'size': 2}
  • id: 107719087
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 166, 'group_counter': 8, 'group_order': 4752, 'label': '33C-14', 'order': 33, 'powers': [155, 47, 154, 9], 'representative': 19647222889, 'size': 2}
  • id: 107719088
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 167, 'group_counter': 8, 'group_order': 4752, 'label': '33C16', 'order': 33, 'powers': [150, 49, 165, 9], 'representative': 16330971852, 'size': 2}
  • id: 107719089
    {'aut_label': '33C1', 'centralizer': '2.b1.a1', 'counter': 168, 'group_counter': 8, 'group_order': 4752, 'label': '33C-16', 'order': 33, 'powers': [149, 49, 166, 10], 'representative': 6757643877, 'size': 2}
  • id: 107719090
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 169, 'group_counter': 8, 'group_order': 4752, 'label': '36A1', 'order': 36, 'powers': [76, 50, 171, 175], 'representative': 18833802974, 'size': 1}
  • id: 107719092
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 170, 'group_counter': 8, 'group_order': 4752, 'label': '36A-1', 'order': 36, 'powers': [77, 51, 172, 176], 'representative': 9573328422, 'size': 1}
  • id: 107719093
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 171, 'group_counter': 8, 'group_order': 4752, 'label': '36A5', 'order': 36, 'powers': [73, 52, 176, 180], 'representative': 22275195544, 'size': 1}
  • id: 107719094
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 172, 'group_counter': 8, 'group_order': 4752, 'label': '36A-5', 'order': 36, 'powers': [72, 53, 175, 179], 'representative': 13327574862, 'size': 1}
  • id: 107719095
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 173, 'group_counter': 8, 'group_order': 4752, 'label': '36A7', 'order': 36, 'powers': [75, 53, 170, 171], 'representative': 5506228112, 'size': 1}
  • id: 107719096
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 174, 'group_counter': 8, 'group_order': 4752, 'label': '36A-7', 'order': 36, 'powers': [74, 52, 169, 172], 'representative': 12138730156, 'size': 1}
  • id: 107719097
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 175, 'group_counter': 8, 'group_order': 4752, 'label': '36A11', 'order': 36, 'powers': [74, 51, 180, 177], 'representative': 12701867122, 'size': 1}
  • id: 107719098
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 176, 'group_counter': 8, 'group_order': 4752, 'label': '36A-11', 'order': 36, 'powers': [75, 50, 179, 178], 'representative': 19334369166, 'size': 1}
  • id: 107719099
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 177, 'group_counter': 8, 'group_order': 4752, 'label': '36A13', 'order': 36, 'powers': [72, 50, 174, 170], 'representative': 11513022416, 'size': 1}
  • id: 107719100
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 178, 'group_counter': 8, 'group_order': 4752, 'label': '36A-13', 'order': 36, 'powers': [73, 51, 173, 169], 'representative': 2565401734, 'size': 1}
  • id: 107719101
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 179, 'group_counter': 8, 'group_order': 4752, 'label': '36A17', 'order': 36, 'powers': [77, 52, 177, 173], 'representative': 15267268856, 'size': 1}
  • id: 107719103
    {'aut_label': '36A1', 'centralizer': '1.a1.a1', 'counter': 180, 'group_counter': 8, 'group_order': 4752, 'label': '36A-17', 'order': 36, 'powers': [76, 53, 178, 174], 'representative': 6006794304, 'size': 1}
  • id: 107719104
    {'aut_label': '36B1', 'centralizer': '2.b1.a1', 'counter': 181, 'group_counter': 8, 'group_order': 4752, 'label': '36B1', 'order': 36, 'powers': [76, 58, 183, 186], 'representative': 6006794509, 'size': 2}
  • id: 107719105
    {'aut_label': '36B1', 'centralizer': '2.b1.a1', 'counter': 182, 'group_counter': 8, 'group_order': 4752, 'label': '36B-1', 'order': 36, 'powers': [77, 59, 184, 185], 'representative': 15267268765, 'size': 2}
  • id: 107719106
    {'aut_label': '36B1', 'centralizer': '2.b1.a1', 'counter': 183, 'group_counter': 8, 'group_order': 4752, 'label': '36B5', 'order': 36, 'powers': [73, 59, 185, 181], 'representative': 2565402049, 'size': 2}
  • id: 107719107
    {'aut_label': '36B1', 'centralizer': '2.b1.a1', 'counter': 184, 'group_counter': 8, 'group_order': 4752, 'label': '36B-5', 'order': 36, 'powers': [72, 58, 186, 182], 'representative': 11513022445, 'size': 2}
  • id: 107719108
    {'aut_label': '36B1', 'centralizer': '2.b1.a1', 'counter': 185, 'group_counter': 8, 'group_order': 4752, 'label': '36B7', 'order': 36, 'powers': [75, 58, 182, 183], 'representative': 19334368945, 'size': 2}
  • id: 107719109
    {'aut_label': '36B1', 'centralizer': '2.b1.a1', 'counter': 186, 'group_counter': 8, 'group_order': 4752, 'label': '36B-7', 'order': 36, 'powers': [74, 59, 181, 184], 'representative': 12701867113, 'size': 2}
  • id: 107719110
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 187, 'group_counter': 8, 'group_order': 4752, 'label': '36C1', 'order': 36, 'powers': [96, 50, 189, 193], 'representative': 19334369158, 'size': 2}
  • id: 107719111
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 188, 'group_counter': 8, 'group_order': 4752, 'label': '36C-1', 'order': 36, 'powers': [97, 51, 190, 194], 'representative': 12701867072, 'size': 2}
  • id: 107719112
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 189, 'group_counter': 8, 'group_order': 4752, 'label': '36C5', 'order': 36, 'powers': [98, 52, 194, 198], 'representative': 15267268968, 'size': 2}
  • id: 107719114
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 190, 'group_counter': 8, 'group_order': 4752, 'label': '36C-5', 'order': 36, 'powers': [99, 53, 193, 197], 'representative': 6006794421, 'size': 2}
  • id: 107719115
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 191, 'group_counter': 8, 'group_order': 4752, 'label': '36C7', 'order': 36, 'powers': [100, 53, 188, 189], 'representative': 13327574737, 'size': 2}
  • id: 107719116
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 192, 'group_counter': 8, 'group_order': 4752, 'label': '36C-7', 'order': 36, 'powers': [101, 52, 187, 190], 'representative': 22275195382, 'size': 2}
  • id: 107719117
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 193, 'group_counter': 8, 'group_order': 4752, 'label': '36C11', 'order': 36, 'powers': [101, 51, 198, 195], 'representative': 2565401896, 'size': 2}
  • id: 107719118
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 194, 'group_counter': 8, 'group_order': 4752, 'label': '36C-11', 'order': 36, 'powers': [100, 50, 197, 196], 'representative': 11513022541, 'size': 2}
  • id: 107719119
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 195, 'group_counter': 8, 'group_order': 4752, 'label': '36C13', 'order': 36, 'powers': [99, 50, 192, 188], 'representative': 18833802857, 'size': 2}
  • id: 107719120
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 196, 'group_counter': 8, 'group_order': 4752, 'label': '36C-13', 'order': 36, 'powers': [98, 51, 191, 187], 'representative': 9573328310, 'size': 2}
  • id: 107719121
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 197, 'group_counter': 8, 'group_order': 4752, 'label': '36C17', 'order': 36, 'powers': [97, 52, 195, 191], 'representative': 12138730206, 'size': 2}
  • id: 107719122
    {'aut_label': '36C1', 'centralizer': '2.b1.a1', 'counter': 198, 'group_counter': 8, 'group_order': 4752, 'label': '36C-17', 'order': 36, 'powers': [96, 53, 196, 192], 'representative': 5506228120, 'size': 2}
  • id: 107719123
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 199, 'group_counter': 8, 'group_order': 4752, 'label': '36D1', 'order': 36, 'powers': [99, 58, 201, 205], 'representative': 13327574950, 'size': 2}
  • id: 107719126
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 200, 'group_counter': 8, 'group_order': 4752, 'label': '36D-1', 'order': 36, 'powers': [98, 59, 202, 206], 'representative': 22275195341, 'size': 2}
  • id: 107719127
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 201, 'group_counter': 8, 'group_order': 4752, 'label': '36D5', 'order': 36, 'powers': [101, 59, 206, 210], 'representative': 12701867275, 'size': 2}
  • id: 107719128
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 202, 'group_counter': 8, 'group_order': 4752, 'label': '36D-5', 'order': 36, 'powers': [100, 58, 205, 209], 'representative': 19334369070, 'size': 2}
  • id: 107719129
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 203, 'group_counter': 8, 'group_order': 4752, 'label': '36D7', 'order': 36, 'powers': [96, 58, 200, 201], 'representative': 18833802761, 'size': 2}
  • id: 107719130
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 204, 'group_counter': 8, 'group_order': 4752, 'label': '36D-7', 'order': 36, 'powers': [97, 59, 199, 202], 'representative': 9573328463, 'size': 2}
  • id: 107719131
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 205, 'group_counter': 8, 'group_order': 4752, 'label': '36D11', 'order': 36, 'powers': [97, 59, 210, 207], 'representative': 15267268815, 'size': 2}
  • id: 107719132
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 206, 'group_counter': 8, 'group_order': 4752, 'label': '36D-11', 'order': 36, 'powers': [96, 58, 209, 208], 'representative': 6006794517, 'size': 2}
  • id: 107719133
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 207, 'group_counter': 8, 'group_order': 4752, 'label': '36D13', 'order': 36, 'powers': [100, 58, 204, 200], 'representative': 5506228208, 'size': 2}
  • id: 107719134
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 208, 'group_counter': 8, 'group_order': 4752, 'label': '36D-13', 'order': 36, 'powers': [101, 59, 203, 199], 'representative': 12138730003, 'size': 2}
  • id: 107719135
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 209, 'group_counter': 8, 'group_order': 4752, 'label': '36D17', 'order': 36, 'powers': [98, 59, 207, 203], 'representative': 2565401937, 'size': 2}
  • id: 107719137
    {'aut_label': '36D1', 'centralizer': '2.b1.a1', 'counter': 210, 'group_counter': 8, 'group_order': 4752, 'label': '36D-17', 'order': 36, 'powers': [99, 58, 208, 204], 'representative': 11513022328, 'size': 2}
  • id: 107719138
    {'aut_label': '36E1', 'centralizer': '66.f1.b1', 'counter': 211, 'group_counter': 8, 'group_order': 4752, 'label': '36E1', 'order': 36, 'powers': [72, 68, 213, 216], 'representative': 5832724, 'size': 66}
  • id: 107719139
    {'aut_label': '36E1', 'centralizer': '66.f1.b1', 'counter': 212, 'group_counter': 8, 'group_order': 4752, 'label': '36E-1', 'order': 36, 'powers': [73, 69, 214, 215], 'representative': 43346048, 'size': 66}
  • id: 107719140
    {'aut_label': '36E1', 'centralizer': '66.f1.b1', 'counter': 213, 'group_counter': 8, 'group_order': 4752, 'label': '36E5', 'order': 36, 'powers': [74, 69, 215, 211], 'representative': 47286273, 'size': 66}
  • id: 107719141
    {'aut_label': '36E1', 'centralizer': '66.f1.b1', 'counter': 214, 'group_counter': 8, 'group_order': 4752, 'label': '36E-5', 'order': 36, 'powers': [75, 68, 216, 212], 'representative': 10560994, 'size': 66}
  • id: 107719142
    {'aut_label': '36E1', 'centralizer': '66.f1.b1', 'counter': 215, 'group_counter': 8, 'group_order': 4752, 'label': '36E7', 'order': 36, 'powers': [76, 68, 212, 213], 'representative': 46180628, 'size': 66}
  • id: 107719143
    {'aut_label': '36E1', 'centralizer': '66.f1.b1', 'counter': 216, 'group_counter': 8, 'group_order': 4752, 'label': '36E-7', 'order': 36, 'powers': [77, 69, 211, 214], 'representative': 34519944, 'size': 66}
  • id: 107719144
    {'aut_label': '36E1', 'centralizer': '66.f1.a1', 'counter': 217, 'group_counter': 8, 'group_order': 4752, 'label': '36F1', 'order': 36, 'powers': [73, 70, 219, 222], 'representative': 15447667, 'size': 66}
  • id: 107719145
    {'aut_label': '36E1', 'centralizer': '66.f1.a1', 'counter': 218, 'group_counter': 8, 'group_order': 4752, 'label': '36F-1', 'order': 36, 'powers': [72, 71, 220, 221], 'representative': 34203535, 'size': 66}
  • id: 107719146
    {'aut_label': '36E1', 'centralizer': '66.f1.a1', 'counter': 219, 'group_counter': 8, 'group_order': 4752, 'label': '36F5', 'order': 36, 'powers': [75, 71, 221, 217], 'representative': 36567670, 'size': 66}
  • id: 107719148
    {'aut_label': '36E1', 'centralizer': '66.f1.a1', 'counter': 220, 'group_counter': 8, 'group_order': 4752, 'label': '36F-5', 'order': 36, 'powers': [74, 70, 222, 218], 'representative': 22540072, 'size': 66}
  • id: 107719149
    {'aut_label': '36E1', 'centralizer': '66.f1.a1', 'counter': 221, 'group_counter': 8, 'group_order': 4752, 'label': '36F7', 'order': 36, 'powers': [77, 70, 218, 219], 'representative': 24588989, 'size': 66}
  • id: 107719150
    {'aut_label': '36E1', 'centralizer': '66.f1.a1', 'counter': 222, 'group_counter': 8, 'group_order': 4752, 'label': '36F-7', 'order': 36, 'powers': [76, 71, 217, 220], 'representative': 54377487, 'size': 66}
  • id: 107719151
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 223, 'group_counter': 8, 'group_order': 4752, 'label': '44A1', 'order': 44, 'powers': [114, 224, 225, 13], 'representative': 125141745, 'size': 2}
  • id: 107719152
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 224, 'group_counter': 8, 'group_order': 4752, 'label': '44A3', 'order': 44, 'powers': [115, 227, 229, 13], 'representative': 500566333, 'size': 2}
  • id: 107719153
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 225, 'group_counter': 8, 'group_order': 4752, 'label': '44A5', 'order': 44, 'powers': [116, 229, 231, 13], 'representative': 2002265071, 'size': 2}
  • id: 107719154
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 226, 'group_counter': 8, 'group_order': 4752, 'label': '44A7', 'order': 44, 'powers': [117, 232, 227, 13], 'representative': 8009059127, 'size': 2}
  • id: 107719155
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 227, 'group_counter': 8, 'group_order': 4752, 'label': '44A9', 'order': 44, 'powers': [118, 230, 223, 13], 'representative': 7195639040, 'size': 2}
  • id: 107719156
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 228, 'group_counter': 8, 'group_order': 4752, 'label': '44A13', 'order': 44, 'powers': [118, 225, 232, 13], 'representative': 15767835078, 'size': 2}
  • id: 107719157
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 229, 'group_counter': 8, 'group_order': 4752, 'label': '44A15', 'order': 44, 'powers': [117, 223, 228, 13], 'representative': 13390145691, 'size': 2}
  • id: 107719159
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 230, 'group_counter': 8, 'group_order': 4752, 'label': '44A17', 'order': 44, 'powers': [116, 226, 224, 13], 'representative': 3879388291, 'size': 2}
  • id: 107719160
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 231, 'group_counter': 8, 'group_order': 4752, 'label': '44A19', 'order': 44, 'powers': [115, 228, 226, 13], 'representative': 15517552093, 'size': 2}
  • id: 107719161
    {'aut_label': '44A1', 'centralizer': '2.b1.a1', 'counter': 232, 'group_counter': 8, 'group_order': 4752, 'label': '44A21', 'order': 44, 'powers': [114, 231, 230, 13], 'representative': 12389013449, 'size': 2}
  • id: 107719162
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 233, 'group_counter': 8, 'group_order': 4752, 'label': '44B1', 'order': 44, 'powers': [114, 235, 237, 11], 'representative': 24715455534, 'size': 2}
  • id: 107719163
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 234, 'group_counter': 8, 'group_order': 4752, 'label': '44B-1', 'order': 44, 'powers': [114, 236, 238, 12], 'representative': 12389013056, 'size': 2}
  • id: 107719164
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 235, 'group_counter': 8, 'group_order': 4752, 'label': '44B3', 'order': 44, 'powers': [115, 241, 239, 12], 'representative': 24340030846, 'size': 2}
  • id: 107719165
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 236, 'group_counter': 8, 'group_order': 4752, 'label': '44B-3', 'order': 44, 'powers': [115, 242, 240, 11], 'representative': 15517551712, 'size': 2}
  • id: 107719166
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 237, 'group_counter': 8, 'group_order': 4752, 'label': '44B5', 'order': 44, 'powers': [116, 239, 236, 11], 'representative': 22838332480, 'size': 2}
  • id: 107719167
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 238, 'group_counter': 8, 'group_order': 4752, 'label': '44B-5', 'order': 44, 'powers': [116, 240, 235, 12], 'representative': 3879387958, 'size': 2}
  • id: 107719168
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 239, 'group_counter': 8, 'group_order': 4752, 'label': '44B7', 'order': 44, 'powers': [117, 233, 242, 12], 'representative': 16831538120, 'size': 2}
  • id: 107719170
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 240, 'group_counter': 8, 'group_order': 4752, 'label': '44B-7', 'order': 44, 'powers': [117, 234, 241, 11], 'representative': 13390145550, 'size': 2}
  • id: 107719171
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 241, 'group_counter': 8, 'group_order': 4752, 'label': '44B9', 'order': 44, 'powers': [118, 238, 233, 11], 'representative': 17644958131, 'size': 2}
  • id: 107719172
    {'aut_label': '44B1', 'centralizer': '2.b1.a1', 'counter': 242, 'group_counter': 8, 'group_order': 4752, 'label': '44B-9', 'order': 44, 'powers': [118, 237, 234, 12], 'representative': 15767834911, 'size': 2}
  • id: 107719173
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 243, 'group_counter': 8, 'group_order': 4752, 'label': '66A1', 'order': 66, 'powers': [136, 114, 244, 18], 'representative': 1877123415, 'size': 2}
  • id: 107719174
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 244, 'group_counter': 8, 'group_order': 4752, 'label': '66A5', 'order': 66, 'powers': [129, 116, 250, 18], 'representative': 1689411121, 'size': 2}
  • id: 107719175
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 245, 'group_counter': 8, 'group_order': 4752, 'label': '66A7', 'order': 66, 'powers': [134, 117, 252, 18], 'representative': 5193374446, 'size': 2}
  • id: 107719176
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 246, 'group_counter': 8, 'group_order': 4752, 'label': '66A13', 'order': 66, 'powers': [131, 118, 243, 18], 'representative': 8572196043, 'size': 2}
  • id: 107719177
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 247, 'group_counter': 8, 'group_order': 4752, 'label': '66A17', 'order': 66, 'powers': [135, 116, 248, 18], 'representative': 10199036245, 'size': 2}
  • id: 107719178
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 248, 'group_counter': 8, 'group_order': 4752, 'label': '66A19', 'order': 66, 'powers': [138, 115, 251, 18], 'representative': 12952150268, 'size': 2}
  • id: 107719179
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 249, 'group_counter': 8, 'group_order': 4752, 'label': '66A23', 'order': 66, 'powers': [130, 114, 247, 18], 'representative': 14140994763, 'size': 2}
  • id: 107719181
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 250, 'group_counter': 8, 'group_order': 4752, 'label': '66A25', 'order': 66, 'powers': [132, 115, 245, 18], 'representative': 8509625417, 'size': 2}
  • id: 107719182
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 251, 'group_counter': 8, 'group_order': 4752, 'label': '66A29', 'order': 66, 'powers': [137, 117, 246, 18], 'representative': 2690543516, 'size': 2}
  • id: 107719183
    {'aut_label': '66A1', 'centralizer': '2.b1.a1', 'counter': 252, 'group_counter': 8, 'group_order': 4752, 'label': '66A31', 'order': 66, 'powers': [133, 118, 249, 18], 'representative': 11951017934, 'size': 2}
  • id: 107719184
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 253, 'group_counter': 8, 'group_order': 4752, 'label': '66B1', 'order': 66, 'powers': [143, 118, 255, 16], 'representative': 18208095085, 'size': 2}
  • id: 107719185
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 254, 'group_counter': 8, 'group_order': 4752, 'label': '66B-1', 'order': 66, 'powers': [144, 118, 256, 17], 'representative': 11951017780, 'size': 2}
  • id: 107719186
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 255, 'group_counter': 8, 'group_order': 4752, 'label': '66B5', 'order': 66, 'powers': [141, 114, 261, 17], 'representative': 4067100275, 'size': 2}
  • id: 107719187
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 256, 'group_counter': 8, 'group_order': 4752, 'label': '66B-5', 'order': 66, 'powers': [142, 114, 262, 16], 'representative': 14140994923, 'size': 2}
  • id: 107719188
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 257, 'group_counter': 8, 'group_order': 4752, 'label': '66B7', 'order': 66, 'powers': [146, 115, 260, 16], 'representative': 16080688950, 'size': 2}
  • id: 107719189
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 258, 'group_counter': 8, 'group_order': 4752, 'label': '66B-7', 'order': 66, 'powers': [145, 115, 259, 17], 'representative': 12952150147, 'size': 2}
  • id: 107719190
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 259, 'group_counter': 8, 'group_order': 4752, 'label': '66B13', 'order': 66, 'powers': [148, 117, 254, 16], 'representative': 17957811894, 'size': 2}
  • id: 107719192
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 260, 'group_counter': 8, 'group_order': 4752, 'label': '66B-13', 'order': 66, 'powers': [147, 117, 253, 17], 'representative': 5193374436, 'size': 2}
  • id: 107719193
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 261, 'group_counter': 8, 'group_order': 4752, 'label': '66B19', 'order': 66, 'powers': [139, 116, 258, 16], 'representative': 1689411034, 'size': 2}
  • id: 107719194
    {'aut_label': '66B1', 'centralizer': '2.b1.a1', 'counter': 262, 'group_counter': 8, 'group_order': 4752, 'label': '66B-19', 'order': 66, 'powers': [140, 116, 257, 17], 'representative': 15642693496, 'size': 2}
  • id: 107719195
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 263, 'group_counter': 8, 'group_order': 4752, 'label': '66C1', 'order': 66, 'powers': [149, 119, 265, 19], 'representative': 6757643488, 'size': 2}
  • id: 107719196
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 264, 'group_counter': 8, 'group_order': 4752, 'label': '66C-1', 'order': 66, 'powers': [150, 120, 266, 20], 'representative': 18646090615, 'size': 2}
  • id: 107719197
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 265, 'group_counter': 8, 'group_order': 4752, 'label': '66C5', 'order': 66, 'powers': [155, 123, 277, 20], 'representative': 19647222952, 'size': 2}
  • id: 107719198
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 266, 'group_counter': 8, 'group_order': 4752, 'label': '66C-5', 'order': 66, 'powers': [156, 124, 278, 19], 'representative': 16956679593, 'size': 2}
  • id: 107719199
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 267, 'group_counter': 8, 'group_order': 4752, 'label': '66C7', 'order': 66, 'powers': [157, 125, 282, 19], 'representative': 10699602290, 'size': 2}
  • id: 107719200
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 268, 'group_counter': 8, 'group_order': 4752, 'label': '66C-7', 'order': 66, 'powers': [158, 126, 281, 20], 'representative': 20773496777, 'size': 2}
  • id: 107719201
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 269, 'group_counter': 8, 'group_order': 4752, 'label': '66C13', 'order': 66, 'powers': [163, 128, 264, 19], 'representative': 23839464883, 'size': 2}
  • id: 107719203
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 270, 'group_counter': 8, 'group_order': 4752, 'label': '66C-13', 'order': 66, 'powers': [164, 127, 263, 20], 'representative': 9197903755, 'size': 2}
  • id: 107719204
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 271, 'group_counter': 8, 'group_order': 4752, 'label': '66C17', 'order': 66, 'powers': [168, 124, 273, 20], 'representative': 16956679603, 'size': 2}
  • id: 107719205
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 272, 'group_counter': 8, 'group_order': 4752, 'label': '66C-17', 'order': 66, 'powers': [167, 123, 274, 19], 'representative': 22150053872, 'size': 2}
  • id: 107719206
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 273, 'group_counter': 8, 'group_order': 4752, 'label': '66C19', 'order': 66, 'powers': [166, 122, 279, 19], 'representative': 22900903173, 'size': 2}
  • id: 107719207
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 274, 'group_counter': 8, 'group_order': 4752, 'label': '66C-19', 'order': 66, 'powers': [165, 121, 280, 20], 'representative': 16268401044, 'size': 2}
  • id: 107719208
    {'aut_label': '66C1', 'centralizer': '2.b1.a1', 'counter': 275, 'group_counter': 8, 'group_order': 4752, 'label': '66C23', 'order': 66, 'powers': [162, 119, 272, 20], 'representative': 11888446874, 'size': 2}
  • id: 107719209
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  • id: 107719210
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  • id: 107719397
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  • id: 107719398
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  • id: 107719400
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  • id: 107719490
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  • id: 107719585
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  • id: 107719586
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  • id: 107719674
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 698, 'group_counter': 8, 'group_order': 4752, 'label': '198B-91', 'order': 198, 'powers': [403, 358, 678, 79], 'representative': 13640428702, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 699, 'group_counter': 8, 'group_order': 4752, 'label': '198B95', 'order': 198, 'powers': [398, 359, 689, 80], 'representative': 3065967924, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 702, 'group_counter': 8, 'group_order': 4752, 'label': '198B-97', 'order': 198, 'powers': [395, 362, 696, 83], 'representative': 24277460102, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 703, 'group_counter': 8, 'group_order': 4752, 'label': '198C1', 'order': 198, 'powers': [420, 343, 705, 84], 'representative': 4192241794, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 704, 'group_counter': 8, 'group_order': 4752, 'label': '198C-1', 'order': 198, 'powers': [419, 344, 706, 85], 'representative': 16581255005, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 705, 'group_counter': 8, 'group_order': 4752, 'label': '198C5', 'order': 198, 'powers': [412, 345, 717, 86], 'representative': 22588049296, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 706, 'group_counter': 8, 'group_order': 4752, 'label': '198C-5', 'order': 198, 'powers': [411, 346, 718, 87], 'representative': 7258209679, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 707, 'group_counter': 8, 'group_order': 4752, 'label': '198C7', 'order': 198, 'powers': [437, 347, 723, 88], 'representative': 23276327758, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 708, 'group_counter': 8, 'group_order': 4752, 'label': '198C-7', 'order': 198, 'powers': [438, 348, 724, 89], 'representative': 7946488228, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 709, 'group_counter': 8, 'group_order': 4752, 'label': '198C13', 'order': 198, 'powers': [396, 349, 741, 87], 'representative': 23026044817, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 710, 'group_counter': 8, 'group_order': 4752, 'label': '198C-13', 'order': 198, 'powers': [395, 350, 742, 86], 'representative': 13702999296, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 711, 'group_counter': 8, 'group_order': 4752, 'label': '198C17', 'order': 198, 'powers': [399, 351, 753, 85], 'representative': 9635899075, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 712, 'group_counter': 8, 'group_order': 4752, 'label': '198C-17', 'order': 198, 'powers': [400, 352, 754, 84], 'representative': 24089747886, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 713, 'group_counter': 8, 'group_order': 4752, 'label': '198C19', 'order': 198, 'powers': [444, 353, 759, 84], 'representative': 18583519710, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 714, 'group_counter': 8, 'group_order': 4752, 'label': '198C-19', 'order': 198, 'powers': [443, 354, 760, 85], 'representative': 22337766092, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 715, 'group_counter': 8, 'group_order': 4752, 'label': '198C23', 'order': 198, 'powers': [434, 355, 752, 86], 'representative': 14829273345, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 716, 'group_counter': 8, 'group_order': 4752, 'label': '198C-23', 'order': 198, 'powers': [433, 356, 751, 87], 'representative': 20648355385, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 717, 'group_counter': 8, 'group_order': 4752, 'label': '198C25', 'order': 198, 'powers': [415, 357, 748, 88], 'representative': 9260474504, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 718, 'group_counter': 8, 'group_order': 4752, 'label': '198C-25', 'order': 198, 'powers': [416, 358, 747, 89], 'representative': 16643825787, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 719, 'group_counter': 8, 'group_order': 4752, 'label': '198C29', 'order': 198, 'powers': [423, 359, 736, 89], 'representative': 4880520341, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 720, 'group_counter': 8, 'group_order': 4752, 'label': '198C-29', 'order': 198, 'powers': [424, 360, 735, 88], 'representative': 20085218189, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 721, 'group_counter': 8, 'group_order': 4752, 'label': '198C31', 'order': 198, 'powers': [418, 361, 730, 87], 'representative': 19084085941, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 722, 'group_counter': 8, 'group_order': 4752, 'label': '198C-31', 'order': 198, 'powers': [417, 362, 729, 86], 'representative': 19709793592, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 724, 'group_counter': 8, 'group_order': 4752, 'label': '198C-35', 'order': 198, 'powers': [407, 361, 715, 84], 'representative': 3003397133, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 726, 'group_counter': 8, 'group_order': 4752, 'label': '198C-37', 'order': 198, 'powers': [442, 359, 709, 85], 'representative': 16894108720, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 728, 'group_counter': 8, 'group_order': 4752, 'label': '198C-41', 'order': 198, 'powers': [450, 357, 708, 87], 'representative': 16768967388, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 730, 'group_counter': 8, 'group_order': 4752, 'label': '198C-43', 'order': 198, 'powers': [394, 355, 712, 89], 'representative': 8259342154, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 735, 'group_counter': 8, 'group_order': 4752, 'label': '198C53', 'order': 198, 'powers': [430, 350, 743, 85], 'representative': 17206962657, 'size': 2}
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    {'aut_label': '198B1', 'centralizer': '2.b1.a1', 'counter': 746, 'group_counter': 8, 'group_order': 4752, 'label': '198C-71', 'order': 198, 'powers': [451, 346, 727, 84], 'representative': 23401469473, 'size': 2}
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    {'aut_label': '198D1', 'centralizer': '2.b1.a1', 'counter': 763, 'group_counter': 8, 'group_order': 4752, 'label': '198D1', 'order': 198, 'powers': [363, 343, 765, 90], 'representative': 18333236492, 'size': 2}
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  • id: 107719764
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  • id: 107719765
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  • id: 107719856
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    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1186, 'group_counter': 8, 'group_order': 4752, 'label': '396D-103', 'order': 396, 'powers': [828, 527, 1196, 201], 'representative': 12764437744, 'size': 2}
  • id: 107718979
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1187, 'group_counter': 8, 'group_order': 4752, 'label': '396D107', 'order': 396, 'powers': [874, 524, 1207, 200], 'representative': 16143259546, 'size': 2}
  • id: 107718980
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1188, 'group_counter': 8, 'group_order': 4752, 'label': '396D-107', 'order': 396, 'powers': [873, 523, 1208, 199], 'representative': 23589181460, 'size': 2}
  • id: 107718981
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1189, 'group_counter': 8, 'group_order': 4752, 'label': '396D109', 'order': 396, 'powers': [863, 526, 1211, 199], 'representative': 14203565569, 'size': 2}
  • id: 107718983
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1190, 'group_counter': 8, 'group_order': 4752, 'label': '396D-109', 'order': 396, 'powers': [864, 525, 1212, 200], 'representative': 9886182141, 'size': 2}
  • id: 107718984
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1191, 'group_counter': 8, 'group_order': 4752, 'label': '396D113', 'order': 396, 'powers': [838, 524, 1225, 201], 'representative': 7007926614, 'size': 2}
  • id: 107718985
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1192, 'group_counter': 8, 'group_order': 4752, 'label': '396D-113', 'order': 396, 'powers': [837, 523, 1226, 202], 'representative': 18958944258, 'size': 2}
  • id: 107718986
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1193, 'group_counter': 8, 'group_order': 4752, 'label': '396D115', 'order': 396, 'powers': [866, 522, 1231, 203], 'representative': 9698469836, 'size': 2}
  • id: 107718987
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1194, 'group_counter': 8, 'group_order': 4752, 'label': '396D-115', 'order': 396, 'powers': [865, 521, 1232, 204], 'representative': 13014720930, 'size': 2}
  • id: 107718988
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1195, 'group_counter': 8, 'group_order': 4752, 'label': '396D119', 'order': 396, 'powers': [843, 520, 1242, 205], 'representative': 21211492071, 'size': 2}
  • id: 107718989
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1196, 'group_counter': 8, 'group_order': 4752, 'label': '396D-119', 'order': 396, 'powers': [844, 519, 1241, 206], 'representative': 19271798266, 'size': 2}
  • id: 107718990
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1197, 'group_counter': 8, 'group_order': 4752, 'label': '396D125', 'order': 396, 'powers': [879, 518, 1224, 209], 'representative': 14516419529, 'size': 2}
  • id: 107718991
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1198, 'group_counter': 8, 'group_order': 4752, 'label': '396D-125', 'order': 396, 'powers': [880, 517, 1223, 210], 'representative': 20022647432, 'size': 2}
  • id: 107718992
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1199, 'group_counter': 8, 'group_order': 4752, 'label': '396D127', 'order': 396, 'powers': [853, 516, 1218, 210], 'representative': 21148921516, 'size': 2}
  • id: 107718995
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1200, 'group_counter': 8, 'group_order': 4752, 'label': '396D-127', 'order': 396, 'powers': [854, 515, 1217, 209], 'representative': 15705264097, 'size': 2}
  • id: 107718996
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1201, 'group_counter': 8, 'group_order': 4752, 'label': '396D131', 'order': 396, 'powers': [850, 514, 1206, 208], 'representative': 24402601656, 'size': 2}
  • id: 107718997
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1202, 'group_counter': 8, 'group_order': 4752, 'label': '396D-131', 'order': 396, 'powers': [849, 513, 1205, 207], 'representative': 15892976512, 'size': 2}
  • id: 107718998
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1203, 'group_counter': 8, 'group_order': 4752, 'label': '396D133', 'order': 396, 'powers': [876, 513, 1200, 206], 'representative': 18708661349, 'size': 2}
  • id: 107718999
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1204, 'group_counter': 8, 'group_order': 4752, 'label': '396D-133', 'order': 396, 'powers': [875, 514, 1199, 205], 'representative': 15329839624, 'size': 2}
  • id: 107719000
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1205, 'group_counter': 8, 'group_order': 4752, 'label': '396D137', 'order': 396, 'powers': [831, 515, 1188, 204], 'representative': 12326442415, 'size': 2}
  • id: 107719001
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1206, 'group_counter': 8, 'group_order': 4752, 'label': '396D-137', 'order': 396, 'powers': [832, 516, 1187, 203], 'representative': 16518684152, 'size': 2}
  • id: 107719002
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1207, 'group_counter': 8, 'group_order': 4752, 'label': '396D139', 'order': 396, 'powers': [840, 517, 1182, 202], 'representative': 10073894519, 'size': 2}
  • id: 107719003
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1208, 'group_counter': 8, 'group_order': 4752, 'label': '396D-139', 'order': 396, 'powers': [839, 518, 1181, 201], 'representative': 24465172460, 'size': 2}
  • id: 107719004
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1209, 'group_counter': 8, 'group_order': 4752, 'label': '396D145', 'order': 396, 'powers': [841, 519, 1164, 199], 'representative': 14578990259, 'size': 2}
  • id: 107719006
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1210, 'group_counter': 8, 'group_order': 4752, 'label': '396D-145', 'order': 396, 'powers': [842, 520, 1163, 200], 'representative': 21962341368, 'size': 2}
  • id: 107719007
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1211, 'group_counter': 8, 'group_order': 4752, 'label': '396D149', 'order': 396, 'powers': [860, 521, 1152, 201], 'representative': 20210359879, 'size': 2}
  • id: 107719008
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1212, 'group_counter': 8, 'group_order': 4752, 'label': '396D-149', 'order': 396, 'powers': [859, 522, 1151, 202], 'representative': 8321912868, 'size': 2}
  • id: 107719009
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1213, 'group_counter': 8, 'group_order': 4752, 'label': '396D151', 'order': 396, 'powers': [877, 523, 1146, 203], 'representative': 23589181556, 'size': 2}
  • id: 107719010
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1214, 'group_counter': 8, 'group_order': 4752, 'label': '396D-151', 'order': 396, 'powers': [878, 524, 1145, 204], 'representative': 16143259484, 'size': 2}
  • id: 107719011
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1215, 'group_counter': 8, 'group_order': 4752, 'label': '396D155', 'order': 396, 'powers': [824, 525, 1132, 205], 'representative': 14891844185, 'size': 2}
  • id: 107719012
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1216, 'group_counter': 8, 'group_order': 4752, 'label': '396D-155', 'order': 396, 'powers': [823, 526, 1131, 206], 'representative': 24527743159, 'size': 2}
  • id: 107719013
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1217, 'group_counter': 8, 'group_order': 4752, 'label': '396D157', 'order': 396, 'powers': [852, 523, 1128, 207], 'representative': 8447054469, 'size': 2}
  • id: 107719014
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1218, 'group_counter': 8, 'group_order': 4752, 'label': '396D-157', 'order': 396, 'powers': [851, 524, 1127, 208], 'representative': 6319648123, 'size': 2}
  • id: 107719015
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1219, 'group_counter': 8, 'group_order': 4752, 'label': '396D161', 'order': 396, 'powers': [857, 527, 1129, 209], 'representative': 11700734731, 'size': 2}
  • id: 107719017
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1220, 'group_counter': 8, 'group_order': 4752, 'label': '396D-161', 'order': 396, 'powers': [858, 528, 1130, 210], 'representative': 14766702566, 'size': 2}
  • id: 107719018
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1221, 'group_counter': 8, 'group_order': 4752, 'label': '396D163', 'order': 396, 'powers': [829, 519, 1135, 210], 'representative': 23714323275, 'size': 2}
  • id: 107719019
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1222, 'group_counter': 8, 'group_order': 4752, 'label': '396D-163', 'order': 396, 'powers': [830, 520, 1136, 209], 'representative': 21211492069, 'size': 2}
  • id: 107719020
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1223, 'group_counter': 8, 'group_order': 4752, 'label': '396D167', 'order': 396, 'powers': [870, 529, 1149, 208], 'representative': 23338898681, 'size': 2}
  • id: 107719021
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1224, 'group_counter': 8, 'group_order': 4752, 'label': '396D-167', 'order': 396, 'powers': [869, 530, 1150, 207], 'representative': 15454981146, 'size': 2}
  • id: 107719022
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1225, 'group_counter': 8, 'group_order': 4752, 'label': '396D169', 'order': 396, 'powers': [867, 517, 1155, 206], 'representative': 20022647426, 'size': 2}
  • id: 107719023
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1226, 'group_counter': 8, 'group_order': 4752, 'label': '396D-169', 'order': 396, 'powers': [868, 518, 1156, 205], 'representative': 24465172475, 'size': 2}
  • id: 107719024
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1227, 'group_counter': 8, 'group_order': 4752, 'label': '396D173', 'order': 396, 'powers': [834, 531, 1167, 204], 'representative': 22462907669, 'size': 2}
  • id: 107719025
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1228, 'group_counter': 8, 'group_order': 4752, 'label': '396D-173', 'order': 396, 'powers': [833, 532, 1168, 203], 'representative': 10887314596, 'size': 2}
  • id: 107719026
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1229, 'group_counter': 8, 'group_order': 4752, 'label': '396D175', 'order': 396, 'powers': [862, 513, 1171, 202], 'representative': 15079556515, 'size': 2}
  • id: 107719028
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1230, 'group_counter': 8, 'group_order': 4752, 'label': '396D-175', 'order': 396, 'powers': [861, 514, 1172, 201], 'representative': 23088615482, 'size': 2}
  • id: 107719029
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1231, 'group_counter': 8, 'group_order': 4752, 'label': '396D179', 'order': 396, 'powers': [847, 531, 1185, 200], 'representative': 18520948970, 'size': 2}
  • id: 107719030
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1232, 'group_counter': 8, 'group_order': 4752, 'label': '396D-179', 'order': 396, 'powers': [848, 532, 1186, 199], 'representative': 17707528933, 'size': 2}
  • id: 107719031
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1233, 'group_counter': 8, 'group_order': 4752, 'label': '396D181', 'order': 396, 'powers': [826, 516, 1191, 199], 'representative': 18020382704, 'size': 2}
  • id: 107719032
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1234, 'group_counter': 8, 'group_order': 4752, 'label': '396D-181', 'order': 396, 'powers': [825, 515, 1192, 200], 'representative': 21649487592, 'size': 2}
  • id: 107719033
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1235, 'group_counter': 8, 'group_order': 4752, 'label': '396D185', 'order': 396, 'powers': [882, 529, 1203, 201], 'representative': 24027177207, 'size': 2}
  • id: 107719034
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1236, 'group_counter': 8, 'group_order': 4752, 'label': '396D-185', 'order': 396, 'powers': [881, 530, 1204, 202], 'representative': 3816817171, 'size': 2}
  • id: 107719035
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1237, 'group_counter': 8, 'group_order': 4752, 'label': '396D191', 'order': 396, 'powers': [846, 527, 1221, 205], 'representative': 11700734603, 'size': 2}
  • id: 107719036
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1238, 'group_counter': 8, 'group_order': 4752, 'label': '396D-191', 'order': 396, 'powers': [845, 528, 1222, 206], 'representative': 8634766758, 'size': 2}
  • id: 107719037
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1239, 'group_counter': 8, 'group_order': 4752, 'label': '396D193', 'order': 396, 'powers': [872, 522, 1227, 207], 'representative': 6820214278, 'size': 2}
  • id: 107719039
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1240, 'group_counter': 8, 'group_order': 4752, 'label': '396D-193', 'order': 396, 'powers': [871, 521, 1228, 208], 'representative': 13014720835, 'size': 2}
  • id: 107719040
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1241, 'group_counter': 8, 'group_order': 4752, 'label': '396D197', 'order': 396, 'powers': [835, 525, 1239, 209], 'representative': 14891844002, 'size': 2}
  • id: 107719041
    {'aut_label': '396D1', 'centralizer': '2.b1.a1', 'counter': 1242, 'group_counter': 8, 'group_order': 4752, 'label': '396D-197', 'order': 396, 'powers': [836, 526, 1240, 210], 'representative': 24527743172, 'size': 2}
• 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: 3782734
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '4752.h', 'group_order': 4752, 'image': None, 'label': '4752.h.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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 3782745
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  • id: 3782756
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  • id: 3782767
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  • id: 3782778
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  • id: 3782789
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  • id: 3782736
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  • id: 3782737
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  • id: 3782738
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  • id: 3782739
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  • id: 3782751
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  • id: 3782752
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  • id: 3782753
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  • id: 3782754
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  • id: 3782755
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  • id: 3782757
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  • id: 3782758
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  • id: 3782759
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  • id: 3782760
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  • id: 3782742
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  • id: 3782743
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  • id: 3782746
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  • id: 3782747
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  • id: 3782748
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  • id: 3782750
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  • id: 3782761
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  • id: 3782764
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  • id: 3782765
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  • id: 3782768
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  • id: 3782769
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  • id: 3782770
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  • id: 3782771
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  • id: 3782772
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  • id: 3782773
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  • id: 3782774
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  • id: 3782775
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  • id: 3782776
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  • id: 3782777
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  • id: 3782779
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  • id: 3782780
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  • id: 3782781
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  • id: 3782782
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  • id: 3782783
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  • id: 3782784
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  • id: 3782786
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  • id: 3782787
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  • id: 3782788
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  • id: 3782790
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  • id: 3782791
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  • id: 3782792
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  • id: 3782793
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  • id: 3782795
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  • id: 3782796
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  • id: 3782797
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  • id: 3782798
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  • id: 3782801
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  • id: 3782802
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  • id: 3782803
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  • id: 3782804
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  • id: 3782805
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  • id: 3782806
    {'cdim': 2, 'counter': 75, 'faithful': True, 'group': '4752.h', 'group_order': 4752, 'image': None, 'label': '4752.h.2ay', 'multiplicity': 120, 'nt': [792, 0], 'qdim': 240, 'qvalues': [240, -240, 0, 0, 0, -120, -120, 60, -120, 60, 0, 0, 0, 0, 0, 120, 120, -60, -180, 0, 180, -60, 0, 0, 120, 180, 0, -180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -24, -24, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 24, 0, 0, 24, 0, 0, 0, 24, 24, 0, -6, 12, -6, 12, -6, 12, -6, -6, 12, -6, 12, 12, -6, 12, -6, 12, 12, 12, 12, -6, -6, -6, 12, -6, -6, -6, 12, 12, -6, -6, 12, -6, 12, 12, -6, 12, -6, 12, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 6, -18, 6, 6, 0, 0, -18, -18, 0, 0, 0, -18, -18, -12, 0, 18, 6, 18, -18, -18, -18, -18, 18, 18, 18, 18, 18, 18, 18, -12, -18, -18, -18, -18, 18, 0, 0, 6, 0, 6, 6, 6, 0, 18, -12, 6, 18, -18, 6, 0, 0, 6, -18, -12, 6, 6, -18, -12, 6, 6, -12, -12, -12, -12, 0, 0, 0, 18, 0, -18, 0, 0, -12, 0, -12, 0, 0, 0, 0, 0, 0, 18, 18, 18, 18, 0, 0, 0, -12, -12, -12, -12, 6, 6, -18, -18, 6, -12, 0, -12, 0, -18, 0, 6, 0, -12, 18, 18, 18, 0, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 3782807
    {'cdim': 2, 'counter': 76, 'faithful': True, 'group': '4752.h', 'group_order': 4752, 'image': None, 'label': '4752.h.2az', 'multiplicity': 120, 'nt': [792, 0], 'qdim': 240, 'qvalues': [240, -240, 0, 0, 0, -120, -120, 60, -120, 60, 0, 0, 0, 0, 0, 120, 120, -60, 180, 0, -180, -60, 0, 0, 120, -180, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -24, -24, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 24, 0, 0, 24, 0, 0, 0, 24, 24, 0, -6, 12, -6, 12, -6, 12, -6, -6, 12, -6, 12, 12, -6, 12, -6, 12, 12, 12, 12, -6, -6, -6, 12, -6, -6, -6, 12, 12, -6, -6, 12, -6, 12, 12, -6, 12, -6, 12, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 6, 18, 6, 6, 0, 0, 18, 18, 0, 0, 0, 18, 18, -12, 0, -18, 6, -18, 18, 18, 18, 18, -18, -18, -18, -18, -18, -18, -18, -12, 18, 18, 18, 18, -18, 0, 0, 6, 0, 6, 6, 6, 0, -18, -12, 6, -18, 18, 6, 0, 0, 6, 18, -12, 6, 6, 18, -12, 6, 6, -12, -12, -12, -12, 0, 0, 0, -18, 0, 18, 0, 0, -12, 0, -12, 0, 0, 0, 0, 0, 0, -18, -18, -18, -18, 0, 0, 0, -12, -12, -12, -12, 6, 6, 18, 18, 6, -12, 0, -12, 0, 18, 0, 6, 0, -12, -18, -18, -18, 0, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}
• group 4752.h does not appear in gps_char
• 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: 60331402
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 4752, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 66, 'label': '4752.h.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4752.h', 'subgroup_hash': 3521362650719687116, 'subgroup_order': 4752, 'subgroup_tex': 'D_{132}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2376, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '2376.g', 'subgroup_hash': 8671729998934366711, 'subgroup_order': 2376, 'subgroup_tex': 'D_{66}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2376, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2376.g', 'subgroup_hash': 8671729998934366711, 'subgroup_order': 2376, 'subgroup_tex': 'D_{66}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 2376, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2376.p', 'subgroup_hash': 1994011958017540, 'subgroup_order': 2376, 'subgroup_tex': 'C_6\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2376, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '2376.t', 'subgroup_hash': 5364163163155265535, 'subgroup_order': 2376, 'subgroup_tex': 'C_{36}\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2376, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.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': '2376.t', 'subgroup_hash': 5364163163155265535, 'subgroup_order': 2376, 'subgroup_tex': 'C_{36}\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 2376, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2376.k', 'subgroup_hash': 6854185121614633591, 'subgroup_order': 2376, 'subgroup_tex': 'C_9\\times D_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 2376, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2376.l', 'subgroup_hash': 5936249624954946874, 'subgroup_order': 2376, 'subgroup_tex': 'C_{132}.C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 1584, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1584.621', 'subgroup_hash': 621, 'subgroup_order': 1584, 'subgroup_tex': 'D_{132}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 792, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1584.135', 'subgroup_hash': 135, 'subgroup_order': 1584, 'subgroup_tex': 'D_{44}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 1188, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1188.64', 'subgroup_hash': 64, 'subgroup_order': 1188, 'subgroup_tex': 'C_6\\times C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1188, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1188.57', 'subgroup_hash': 57, 'subgroup_order': 1188, 'subgroup_tex': 'C_9\\times D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1188, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.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': '1188.57', 'subgroup_hash': 57, 'subgroup_order': 1188, 'subgroup_tex': 'C_9\\times D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 1188, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1188.26', 'subgroup_hash': 26, 'subgroup_order': 1188, 'subgroup_tex': 'C_3\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 1188, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1188.26', 'subgroup_hash': 26, 'subgroup_order': 1188, 'subgroup_tex': 'C_3\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1188, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '1188.19', 'subgroup_hash': 19, 'subgroup_order': 1188, 'subgroup_tex': 'C_{33}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1188, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '1188.19', 'subgroup_hash': 19, 'subgroup_order': 1188, 'subgroup_tex': 'C_{33}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 792, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.94', 'subgroup_hash': 94, 'subgroup_order': 792, 'subgroup_tex': 'D_{66}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 792, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.94', 'subgroup_hash': 94, 'subgroup_order': 792, 'subgroup_tex': 'D_{66}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 792, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.105', 'subgroup_hash': 105, 'subgroup_order': 792, 'subgroup_tex': 'C_6\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 792, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '792.28', 'subgroup_hash': 28, 'subgroup_order': 792, 'subgroup_tex': 'C_2\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 792, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.91', 'subgroup_hash': 91, 'subgroup_order': 792, 'subgroup_tex': 'C_{12}\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 792, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.91', 'subgroup_hash': 91, 'subgroup_order': 792, 'subgroup_tex': 'C_{12}\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 792, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.92', 'subgroup_hash': 92, 'subgroup_order': 792, 'subgroup_tex': 'C_3\\times D_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 792, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '792.90', 'subgroup_hash': 90, 'subgroup_order': 792, 'subgroup_tex': 'C_{132}.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.17', 'subgroup_hash': 17, 'subgroup_order': 792, 'subgroup_tex': 'C_{99}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.17', 'subgroup_hash': 17, 'subgroup_order': 792, 'subgroup_tex': 'C_{99}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 264, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.28', 'subgroup_hash': 28, 'subgroup_order': 792, 'subgroup_tex': 'C_2\\times C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.14', 'subgroup_hash': 14, 'subgroup_order': 792, 'subgroup_tex': 'D_{11}\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331598
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.14', 'subgroup_hash': 14, 'subgroup_order': 792, 'subgroup_tex': 'D_{11}\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.15', 'subgroup_hash': 15, 'subgroup_order': 792, 'subgroup_tex': 'C_9\\times D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60331600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '792.13', 'subgroup_hash': 13, 'subgroup_order': 792, 'subgroup_tex': 'C_{99}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 594, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '594.20', 'subgroup_hash': 20, 'subgroup_order': 594, 'subgroup_tex': 'C_3\\times C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 297, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '594.20', 'subgroup_hash': 20, 'subgroup_order': 594, 'subgroup_tex': 'C_3\\times C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 297, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '594.13', 'subgroup_hash': 13, 'subgroup_order': 594, 'subgroup_tex': 'C_9\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 297, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '594.13', 'subgroup_hash': 13, 'subgroup_order': 594, 'subgroup_tex': 'C_9\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 528, 'counter': 37, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '4752.h.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.149', 'subgroup_hash': 149, 'subgroup_order': 528, 'subgroup_tex': 'D_{132}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60331606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 264, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '528.129', 'subgroup_hash': 129, 'subgroup_order': 528, 'subgroup_tex': 'D_{44}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 216, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '4752.h.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.347', 'subgroup_hash': 347, 'subgroup_order': 432, 'subgroup_tex': 'D_{12}:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 396, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.30', 'subgroup_hash': 30, 'subgroup_order': 396, 'subgroup_tex': 'C_6\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 396, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.10', 'subgroup_hash': 10, 'subgroup_order': 396, 'subgroup_tex': 'C_2\\times C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331611
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.27', 'subgroup_hash': 27, 'subgroup_order': 396, 'subgroup_tex': 'C_3\\times D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.27', 'subgroup_hash': 27, 'subgroup_order': 396, 'subgroup_tex': 'C_3\\times D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 396, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.16', 'subgroup_hash': 16, 'subgroup_order': 396, 'subgroup_tex': 'C_3\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 396, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.16', 'subgroup_hash': 16, 'subgroup_order': 396, 'subgroup_tex': 'C_3\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.13', 'subgroup_hash': 13, 'subgroup_order': 396, 'subgroup_tex': 'C_{33}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 396, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.13', 'subgroup_hash': 13, 'subgroup_order': 396, 'subgroup_tex': 'C_{33}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331617
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 396, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331618
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 396, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 132, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.10', 'subgroup_hash': 10, 'subgroup_order': 396, 'subgroup_tex': 'C_2\\times C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 198, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.7', 'subgroup_hash': 7, 'subgroup_order': 396, 'subgroup_tex': 'C_9\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331622
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 198, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.7', 'subgroup_hash': 7, 'subgroup_order': 396, 'subgroup_tex': 'C_9\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331623
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 132, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331624
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 132, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.4', 'subgroup_hash': 4, 'subgroup_order': 396, 'subgroup_tex': 'C_{396}', 'supersolvable': True, 'sylow': 0}
  • id: 60331625
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 198, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.2', 'subgroup_hash': 2, 'subgroup_order': 396, 'subgroup_tex': 'C_{11}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331626
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 198, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '396.2', 'subgroup_hash': 2, 'subgroup_order': 396, 'subgroup_tex': 'C_{11}:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 297, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 33, 'label': '4752.h.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '297.2', 'subgroup_hash': 2, 'subgroup_order': 297, 'subgroup_tex': 'C_3\\times C_{99}', 'supersolvable': True, 'sylow': 0}
  • id: 60331628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 264, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.27', 'subgroup_hash': 27, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 264, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.27', 'subgroup_hash': 27, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 264, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.28', 'subgroup_hash': 28, 'subgroup_order': 264, 'subgroup_tex': 'C_2\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 264, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.28', 'subgroup_hash': 28, 'subgroup_order': 264, 'subgroup_tex': 'C_2\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 264, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.24', 'subgroup_hash': 24, 'subgroup_order': 264, 'subgroup_tex': 'C_4\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 264, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.24', 'subgroup_hash': 24, 'subgroup_order': 264, 'subgroup_tex': 'C_4\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 264, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.25', 'subgroup_hash': 25, 'subgroup_order': 264, 'subgroup_tex': 'D_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 264, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.23', 'subgroup_hash': 23, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.17', 'subgroup_hash': 17, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.17', 'subgroup_hash': 17, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 88, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.28', 'subgroup_hash': 28, 'subgroup_order': 264, 'subgroup_tex': 'C_2\\times C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.14', 'subgroup_hash': 14, 'subgroup_order': 264, 'subgroup_tex': 'C_{12}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.14', 'subgroup_hash': 14, 'subgroup_order': 264, 'subgroup_tex': 'C_{12}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.15', 'subgroup_hash': 15, 'subgroup_order': 264, 'subgroup_tex': 'C_3\\times D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60331644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '264.13', 'subgroup_hash': 13, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331645
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 216, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '22.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 22, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.73', 'subgroup_hash': 73, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.58', 'subgroup_hash': 58, 'subgroup_order': 216, 'subgroup_tex': 'D_6:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.22.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.58', 'subgroup_hash': 58, 'subgroup_order': 216, 'subgroup_tex': 'D_6:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.47', 'subgroup_hash': 47, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.22.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.47', 'subgroup_hash': 47, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.22.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.48', 'subgroup_hash': 48, 'subgroup_order': 216, 'subgroup_tex': 'C_9\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.22.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.44', 'subgroup_hash': 44, 'subgroup_order': 216, 'subgroup_tex': 'C_{12}.C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 198, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '198.10', 'subgroup_hash': 10, 'subgroup_order': 198, 'subgroup_tex': 'C_3\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331654
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 198, 'counter': 81, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331655
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 66, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331656
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 99, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.10', 'subgroup_hash': 10, 'subgroup_order': 198, 'subgroup_tex': 'C_3\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331657
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 99, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331658
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 33, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331659
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 33, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.4', 'subgroup_hash': 4, 'subgroup_order': 198, 'subgroup_tex': 'C_{198}', 'supersolvable': True, 'sylow': 0}
  • id: 60331660
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 99, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.2', 'subgroup_hash': 2, 'subgroup_order': 198, 'subgroup_tex': 'C_9\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331661
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 99, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.2', 'subgroup_hash': 2, 'subgroup_order': 198, 'subgroup_tex': 'C_9\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 99, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.7', 'subgroup_hash': 7, 'subgroup_order': 198, 'subgroup_tex': 'C_3\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331664
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 99, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '198.7', 'subgroup_hash': 7, 'subgroup_order': 198, 'subgroup_tex': 'C_3\\times D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 88, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 22, 'label': '4752.h.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '176.30', 'subgroup_hash': 30, 'subgroup_order': 176, 'subgroup_tex': 'D_{44}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60331666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.33.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '33.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.50', 'subgroup_hash': 50, 'subgroup_order': 144, 'subgroup_tex': 'D_4:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.33.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '33.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.161', 'subgroup_hash': 161, 'subgroup_order': 144, 'subgroup_tex': 'D_{12}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 132, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.10', 'subgroup_hash': 10, 'subgroup_order': 132, 'subgroup_tex': 'C_2\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 132, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.10', 'subgroup_hash': 10, 'subgroup_order': 132, 'subgroup_tex': 'C_2\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.9', 'subgroup_hash': 9, 'subgroup_order': 132, 'subgroup_tex': 'D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.9', 'subgroup_hash': 9, 'subgroup_order': 132, 'subgroup_tex': 'D_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331672
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 132, 'counter': 98, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331673
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 132, 'counter': 99, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 132, 'counter': 100, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331405
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 132, 'counter': 101, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331406
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.3', 'subgroup_hash': 3, 'subgroup_order': 132, 'subgroup_tex': 'C_{33}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331407
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 132, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.36.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.3', 'subgroup_hash': 3, 'subgroup_order': 132, 'subgroup_tex': 'C_{33}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 44, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.10', 'subgroup_hash': 10, 'subgroup_order': 132, 'subgroup_tex': 'C_2\\times C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 66, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 66, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.36.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331411
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 66, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.2', 'subgroup_hash': 2, 'subgroup_order': 132, 'subgroup_tex': 'C_{11}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331412
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 66, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.36.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.2', 'subgroup_hash': 2, 'subgroup_order': 132, 'subgroup_tex': 'C_{11}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331413
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 44, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331415
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 44, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
  • id: 60331416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 108, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.29', 'subgroup_hash': 29, 'subgroup_order': 108, 'subgroup_tex': 'C_6\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 108, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331418
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 108, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.44.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.12', 'subgroup_hash': 12, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.44.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.44.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.24', 'subgroup_hash': 24, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.44.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.44.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331423
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 99, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '99.2', 'subgroup_hash': 2, 'subgroup_order': 99, 'subgroup_tex': 'C_3\\times C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331424
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 99, 'counter': 119, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '99.1', 'subgroup_hash': 1, 'subgroup_order': 99, 'subgroup_tex': 'C_{99}', 'supersolvable': True, 'sylow': 0}
  • id: 60331426
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 33, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '99.1', 'subgroup_hash': 1, 'subgroup_order': 99, 'subgroup_tex': 'C_{99}', 'supersolvable': True, 'sylow': 0}
  • id: 60331427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 88, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.8', 'subgroup_hash': 8, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60331428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.54.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60331433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 44, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 72, 'counter': 128, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.66.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '66.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '66.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 66, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 72, 'counter': 129, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.66.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '66.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '66.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 66, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{33}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60331440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60331441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 24, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.9', 'subgroup_hash': 9, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.66.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.11', 'subgroup_hash': 11, 'subgroup_order': 72, 'subgroup_tex': 'Q_8\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331451
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 66, 'counter': 143, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331452
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 66, 'counter': 144, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.18', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 18, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331453
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 22, 'counter': 145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331454
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 33, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331455
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 33, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331456
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 11, 'counter': 148, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331457
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 11, 'counter': 149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.72.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
  • id: 60331459
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 33, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331460
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 33, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.72.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331461
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 33, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.3', 'subgroup_hash': 3, 'subgroup_order': 66, 'subgroup_tex': 'D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331462
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 33, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.3', 'subgroup_hash': 3, 'subgroup_order': 66, 'subgroup_tex': 'D_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331463
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 54, 'counter': 154, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '88.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331464
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 27, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.88.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331465
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.88.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.88.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.99.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '99.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': 99, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331468
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.99.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '99.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': 99, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60331470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 44, 'counter': 160, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.24', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331471
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 44, 'counter': 161, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.24', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60331472
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 44, 'counter': 162, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.24', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 60331473
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 22, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331474
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 22, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.108.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331475
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 22, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331476
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 22, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.108.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 36, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 60331478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 36, 'counter': 168, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.132.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 36, 'counter': 169, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.132.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 36, 'counter': 170, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.132.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331482
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 36, 'counter': 171, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.132.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{66}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331483
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 36, 'counter': 172, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.132.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 12, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331486
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 60331488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 60331489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 60331490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.132.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 60331492
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 12, 'counter': 180, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.132.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331493
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 12, 'counter': 181, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.132.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331494
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 182, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.132.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331495
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 183, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.132.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 60331496
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 33, 'counter': 184, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331497
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 33, 'counter': 185, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331498
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 11, 'counter': 186, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
  • id: 60331499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 27, 'counter': 187, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '4752.h.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '176.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '176.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 3}
  • id: 60331500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 24, 'counter': 188, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.198.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '198.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '198.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 198, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{33}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 60331501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 24, 'counter': 189, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.198.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '198.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '198.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 198, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60331503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 8, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': 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: 60331508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': 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: 60331509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': 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: 60331510
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': 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: 60331512
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': 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: 60331515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.198.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '198.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': 198, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331518
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 22, 'counter': 203, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.109', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 109, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331519
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 11, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 60331520
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 11, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331521
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 11, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.216.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 60331522
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 18, 'counter': 207, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 60331523
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 18, 'counter': 208, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.264.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331524
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 6, 'counter': 209, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.264.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 9, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.264.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 60331527
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 9, 'counter': 211, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.264.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331528
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 3, 'counter': 212, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.264.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 3, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.264.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331530
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.264.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331531
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 215, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.264.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 60331532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.264.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 60331533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.264.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 60331534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '4752.h.297.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '297.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': 297, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 2}
  • id: 60331535
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 12, 'counter': 219, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.396.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331537
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 12, 'counter': 220, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.396.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 12, 'counter': 221, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.396.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 12, 'counter': 222, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.396.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331540
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 12, 'counter': 223, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.396.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 12, 'counter': 224, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.396.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 60331542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331548
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 230, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.396.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.396.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331550
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331551
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.396.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331552
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 4, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.396.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331553
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 4, 'counter': 235, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.396.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '396.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': 396, 'quotient_simple': 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: 60331554
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 11, 'counter': 236, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '4752.h.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.347', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 347, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:C_{18}', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 60331555
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 9, 'counter': 237, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.528.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '528.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '528.129', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 129, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 528, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 60331556
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 9, 'counter': 238, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '4752.h.528.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '528.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '528.149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 149, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 528, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{132}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331557
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 3, 'counter': 239, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.528.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 60331559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 8, 'counter': 240, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.594.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '594.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '594.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 594, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{33}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 60331560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.594.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '594.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': 594, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.594.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '594.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 594, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331562
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.594.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '594.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': 594, 'quotient_simple': 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: 60331563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.594.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '594.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 594, 'quotient_simple': 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: 60331564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.594.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '594.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': 594, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.594.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '594.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': 594, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 60331566
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 6, 'counter': 247, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.792.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '792.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.134', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 134, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 792, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331567
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 6, 'counter': 248, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.792.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '792.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 792, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 60331568
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331570
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 3, 'counter': 250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331571
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 3, 'counter': 251, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331572
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331573
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331574
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 254, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331575
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 255, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.792.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331576
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.792.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331577
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.792.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '792.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': 792, 'quotient_simple': 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: 60331578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 4, 'counter': 258, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4752.h.1188.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1188.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1188.57', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 57, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1188, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 60331579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 4, 'counter': 259, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.1188.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1188.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1188.57', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 57, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1188, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 4, 'counter': 260, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.1188.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1188.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1188.57', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 57, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1188, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9\\times D_{66}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 60331582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.1188.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1188.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': 1188, 'quotient_simple': 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: 60331583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '4752.h.1188.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1188.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': 1188, 'quotient_simple': 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: 60331584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.1188.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1188.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': 1188, 'quotient_simple': 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: 60331585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.1188.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1188.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': 1188, 'quotient_simple': 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: 60331586
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 3, 'counter': 265, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.1584.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1584.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1584.621', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 621, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1584, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{132}:C_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 60331587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': True, 'core_order': 3, 'counter': 266, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.1584.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1584.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1584.135', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 135, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1584, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{44}:C_{18}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 60331588
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.1584.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1584.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': 1584, '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: 60331589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 2, 'counter': 268, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4752.h.2376.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2376.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5394951545398917477, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2376, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:(C_2\\times C_{18}\\times S_3)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 60331590
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 2376, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.2376.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2376.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': 2376, '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: 60331592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.2376.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2376.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': 2376, '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: 60331593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '4752.h.2376.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2376.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2376, '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: 60331594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4752.h', 'ambient_counter': 8, 'ambient_order': 4752, 'ambient_tex': 'D_{132}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 4752, 'characteristic': True, 'core_order': 1, 'counter': 272, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '4752.h.4752.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4752.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '4752.h', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3521362650719687116, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 4752, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{132}:C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C8'], '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: 60331413
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.h1.a1'], 'contains': ['72.c1.a1', '108.b1.a1', '396.l1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [9323045302, 7883917508, 24590313888, 23839464637], 'label': '4752.h.36.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.l1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331431
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.i1.b1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.d1.b1', '108.e1.a1', '594.c1.b1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [57355781, 24590313888, 60343206, 23839464637], 'label': '4752.h.54.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.c1.b1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331402
    {'ambient': '4752.h', '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': '132.e1.a1', 'complements': ['4752.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1', '3.b1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 22713190600, 24590313888, 23839464637, 19647222832, 3378821867, 158006], 'label': '4752.h.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.e1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '132.9', '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': '132.9'}
  • id: 60331403
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '6.g1.a1', '6.g1.b1', '6.i1.a1', '6.i1.b1', '6.j1.a1', '6.k1.a1', '9.b1.a1', '33.a1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 17644958238, 2690543349, 13640428742, 24590313888, 23839464637, 158006], 'label': '4752.h.3.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331404
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '36.f1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.c1.a1', '18.d1.a1', '18.d1.b1'], 'contains': ['72.b1.a1', '108.b1.a1', '396.e1.a1'], 'core': '36.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 21461775264, 23839464637, 19647222832], 'label': '4752.h.36.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.f1.a1', 'normal_contained_in': ['12.d1.a1', '18.c1.a1', '18.d1.a1', '18.d1.b1'], 'normal_contains': ['72.b1.a1', '108.b1.a1', '396.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331405
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '36.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.c1.a1', '18.e1.a1', '18.f1.a1'], 'contains': ['72.b1.a1', '108.c1.a1', '396.f1.a1'], 'core': '36.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.36.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.g1.a1', 'normal_contained_in': ['12.e1.a1', '18.c1.a1', '18.e1.a1', '18.f1.a1'], 'normal_contains': ['72.b1.a1', '108.c1.a1', '396.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.g1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331406
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.a1.a1', '18.d1.b1', '18.f1.a1'], 'contains': ['72.b1.a1', '108.e1.a1', '396.k1.a1'], 'core': '36.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [57355781, 24590313888, 23839464637, 19647222832], 'label': '4752.h.36.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.a1', 'normal_contained_in': ['12.f1.a1', '18.a1.a1', '18.d1.b1', '18.f1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331407
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '18.a1.b1', '18.d1.a1', '18.f1.a1'], 'contains': ['72.b1.a1', '108.e1.b1', '396.k1.b1'], 'core': '36.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637, 19647222832, 23638174], 'label': '4752.h.36.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.b1', 'normal_contained_in': ['12.f1.b1', '18.a1.b1', '18.d1.a1', '18.f1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331408
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.h1.a1'], 'contains': ['72.c1.a1', '72.f1.a1', '72.f1.b1', '108.a1.a1', '396.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888, 23839464637], 'label': '4752.h.36.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331409
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.j1.a1', '18.g1.a1', '18.i1.a1', '18.j1.a1'], 'contains': ['72.a1.a1', '72.g1.a1', '108.d1.a1', '396.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 24590313888, 23839464637, 158006], 'label': '4752.h.36.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.j1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331410
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.j1.b1', '18.g1.b1', '18.i1.b1', '18.j1.a1'], 'contains': ['72.a1.a1', '72.g1.b1', '108.d1.b1', '396.h1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 8560511, 24590313888, 23839464637], 'label': '4752.h.36.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.j1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331411
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.m1.a1', '18.g1.a1', '18.i1.b1', '18.k1.a1'], 'contains': ['72.a1.a1', '108.e1.a1', '396.j1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 24590313888, 23839464637, 57212464], 'label': '4752.h.36.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.k1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331412
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '12.m1.b1', '18.g1.b1', '18.i1.a1', '18.k1.a1'], 'contains': ['72.a1.a1', '108.e1.b1', '396.j1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [23533366, 16330971943, 24590313888, 23839464637], 'label': '4752.h.36.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.k1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331414
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '240.208', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '12.a1.a1', '12.b1.a1', '12.i1.a1', '44.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 22713190600, 24590313888, 23839464637, 19647222832], 'label': '4752.h.4.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331415
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.h1.a1'], 'contains': ['72.c1.a1', '108.c1.a1', '396.m1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [17644958238, 22650619827, 24590313888, 23839464637], 'label': '4752.h.36.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331416
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '44.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.a1', '22.b1.a1', '22.b1.b1'], 'contains': ['88.a1.a1', '88.b1.a1', '132.a1.a1', '132.b1.a1', '132.g1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 19522081488, 2127406644], 'label': '4752.h.44.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.a1.a1', 'normal_contained_in': ['4.a1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.a1.a1', '132.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.2', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331417
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '44.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.a1.a1', '22.c1.a1', '22.c1.b1'], 'contains': ['88.a1.a1', '132.c1.a1', '132.e1.a1', '132.k1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 20898638422, 19522081488, 2127406644], 'label': '4752.h.44.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.b1.a1', 'normal_contained_in': ['4.c1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.c1.a1', '132.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.2', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331418
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '44.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '22.a1.a1', '22.d1.a1', '22.e1.a1'], 'contains': ['88.a1.a1', '132.d1.a1', '132.f1.a1', '132.l1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 11075027061, 19522081488, 2127406644], 'label': '4752.h.44.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.c1.a1', 'normal_contained_in': ['4.d1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.d1.a1', '132.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.c1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '22.2', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331419
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '72.48', 'aut_weyl_index': 880, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.b1.a1', '22.c1.a1', '22.d1.a1'], 'contains': ['88.a1.a1', '88.c1.a1', '132.h1.a1', '132.i1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 19522081488, 2127406644, 158006], 'label': '4752.h.44.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.d1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331420
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '72.48', 'aut_weyl_index': 880, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '22.b1.b1', '22.c1.b1', '22.d1.a1'], 'contains': ['88.a1.a1', '88.c1.b1', '132.h1.b1', '132.i1.b1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 8560511, 19522081488, 2127406644], 'label': '4752.h.44.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.d1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331421
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '72.48', 'aut_weyl_index': 880, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '22.b1.a1', '22.c1.b1', '22.e1.a1'], 'contains': ['88.a1.a1', '132.j1.a1', '132.m1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 57212464, 19522081488, 2127406644], 'label': '4752.h.44.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.e1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331422
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '72.48', 'aut_weyl_index': 880, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '22.b1.b1', '22.c1.a1', '22.e1.a1'], 'contains': ['88.a1.a1', '132.j1.b1', '132.m1.b1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [23533366, 24778026504, 22650619827, 19522081488, 2127406644], 'label': '4752.h.44.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.e1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331423
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '48.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.h1.a1', '24.h1.b1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '528.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 19647222832], 'label': '4752.h.48.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1', '144.b1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '1584.621', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.9', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331424
    {'ambient': '4752.h', 'aut_centralizer_order': 1056, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': ['99.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1', '24.g1.a1', '24.g1.b1'], 'contains': ['144.a1.a1', '528.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888], 'label': '4752.h.48.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.a1'], 'normal_contains': ['144.a1.a1', '528.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '528.149', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.9', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331425
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.c1.a1', '12.j1.a1', '44.d1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.4.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331426
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1', '24.f1.a1', '24.f1.b1'], 'contains': ['144.a1.a1', '528.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 10511889933, 24590313888], 'label': '4752.h.48.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331427
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': ['88.c1.a1', '88.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.c1.a1', '18.h1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '594.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [17644958238, 24778026109, 24590313888, 23839464637], 'label': '4752.h.54.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.b1.a1', '18.c1.a1'], 'normal_contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '594.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331428
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.d1.a1', '108.e1.a1', '594.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [24778026109, 24590313888, 23839464637, 158006], 'label': '4752.h.54.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331429
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '18.g1.b1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.d1.b1', '108.e1.b1', '594.b1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [24778026109, 8560511, 24590313888, 23839464637], 'label': '4752.h.54.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331430
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '440.42', 'aut_weyl_index': 144, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.i1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.d1.a1', '108.e1.b1', '594.c1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [24590313888, 23839464637, 7195639147, 158006], 'label': '4752.h.54.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.c1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331577
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '792.h1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10560, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.b1', '264.h1.b1', '396.i1.b1'], 'contains': ['1584.b1.a1', '2376.c1.b1'], 'core': '1584.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': None, 'generators': [8560511, 2127406644], 'label': '4752.h.792.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.b1', 'old_label': '792.h1.b1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60331432
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 72, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.j1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.d1.a1', '108.d1.b1', '594.d1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [17644958238, 24590313888, 23839464637, 158006], 'label': '4752.h.54.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331433
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '880.118', 'aut_weyl_index': 72, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.k1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.e1.a1', '108.e1.b1', '594.e1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [17644958238, 57355781, 24590313888, 23839464637], 'label': '4752.h.54.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331434
    {'ambient': '4752.h', 'aut_centralizer_order': 3960, 'aut_label': '66.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 3960, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '22.a1.a1', '33.b1.a1'], 'contains': ['132.a1.a1', '132.c1.a1', '132.d1.a1', '198.a1.a1', '198.b1.a1', '198.e1.a1'], 'core': '66.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 11075027061, 2127406644], 'label': '4752.h.66.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '66.a1.a1', 'normal_contained_in': ['6.b1.a1', '22.a1.a1'], 'normal_contains': ['132.a1.a1', '132.c1.a1', '132.d1.a1', '198.a1.a1', '198.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '33.1', 'quotient_action_kernel_order': 33, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331435
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '66.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': ['72.h1.a1', '72.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '22.a1.a1', '33.a1.a1'], 'contains': ['132.b1.a1', '132.e1.a1', '132.f1.a1', '198.a1.a1'], 'core': '66.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 2189977417, 19522081488], 'label': '4752.h.66.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '66.b1.a1', 'normal_contained_in': ['6.c1.a1', '22.a1.a1'], 'normal_contains': ['132.b1.a1', '132.e1.a1', '132.f1.a1', '198.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '66.b1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '33.1', 'quotient_action_kernel_order': 33, 'quotient_fusion': None, 'short_label': '66.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331436
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'contains': ['8.a1.a1', '8.c1.b1', '12.c1.b1', '12.j1.b1', '44.d1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 8560511, 24590313888, 23839464637, 19647222832], 'label': '4752.h.4.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.d1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331437
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '66.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '22.b1.a1', '33.a1.a1'], 'contains': ['132.b1.a1', '132.h1.a1', '132.m1.a1', '198.c1.a1'], 'core': '132.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 2189977417, 19522081488, 158006], 'label': '4752.h.66.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.c1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331438
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '66.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.b1', '22.b1.b1', '33.a1.a1'], 'contains': ['132.b1.a1', '132.h1.b1', '132.m1.b1', '198.c1.b1'], 'core': '132.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 8560511, 2189977417, 19522081488], 'label': '4752.h.66.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.c1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331439
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '66.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '48.51', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.b1.a1', '33.b1.a1'], 'contains': ['132.a1.a1', '132.i1.a1', '132.j1.a1', '198.c1.a1', '198.d1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 2127406644, 158006], 'label': '4752.h.66.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.d1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331440
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '66.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '48.51', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '22.b1.b1', '33.b1.a1'], 'contains': ['132.a1.a1', '132.i1.b1', '132.j1.b1', '198.c1.b1', '198.d1.b1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 8560511, 2127406644], 'label': '4752.h.66.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.d1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331441
    {'ambient': '4752.h', 'aut_centralizer_order': 1320, 'aut_label': '66.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '22.a1.a1'], 'contains': ['132.g1.a1', '132.k1.a1', '132.l1.a1', '198.a1.a1'], 'core': '198.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 17895241274, 2189977417], 'label': '4752.h.66.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '66.e1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331442
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '66.f1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '22.c1.a1', '33.a1.a1'], 'contains': ['132.e1.a1', '132.h1.a1', '132.m1.b1', '198.f1.a1'], 'core': '132.e1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 19522081488, 13765570280, 158006], 'label': '4752.h.66.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.f1.a1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331443
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '66.f1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2640, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '22.c1.b1', '33.a1.a1'], 'contains': ['132.e1.a1', '132.h1.b1', '132.m1.a1', '198.f1.b1'], 'core': '132.e1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 57212464, 19522081488, 27992073], 'label': '4752.h.66.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.f1.b1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331444
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '66.g1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '48.45', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '22.d1.a1', '33.a1.a1'], 'contains': ['132.f1.a1', '132.h1.a1', '132.h1.b1', '198.g1.a1'], 'core': '132.f1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 19522081488, 158006], 'label': '4752.h.66.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.g1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331445
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '66.h1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '48.51', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '22.c1.a1', '33.b1.a1'], 'contains': ['132.c1.a1', '132.i1.a1', '132.j1.b1', '198.f1.a1', '198.h1.a1'], 'core': '132.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 20898638422, 2127406644, 158006], 'label': '4752.h.66.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.h1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331446
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '66.h1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '48.51', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '22.c1.b1', '33.b1.a1'], 'contains': ['132.c1.a1', '132.i1.b1', '132.j1.a1', '198.f1.b1', '198.h1.b1'], 'core': '132.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 57212464, 2127406644, 27992073], 'label': '4752.h.66.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.h1.b1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331447
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '240.208', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'contains': ['8.a1.a1', '12.d1.a1', '12.g1.a1', '12.k1.a1', '44.b1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9323045302, 22650619827, 13640428742, 24590313888, 23839464637, 19647222832], 'label': '4752.h.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.c1.b1'], 'normal_contains': ['8.a1.a1', '12.d1.a1', '12.g1.a1', '44.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331448
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '66.i1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 660, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '22.d1.a1', '33.b1.a1'], 'contains': ['132.d1.a1', '132.i1.a1', '132.i1.b1', '198.g1.a1', '198.i1.a1'], 'core': '132.d1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 11075027061, 2127406644, 158006], 'label': '4752.h.66.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.i1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331449
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '66.j1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 660, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '22.e1.a1', '33.b1.a1'], 'contains': ['132.d1.a1', '132.j1.a1', '132.j1.b1', '198.j1.a1', '198.k1.a1'], 'core': '132.d1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 11075027061, 57212464, 2127406644], 'label': '4752.h.66.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.j1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331450
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '66.k1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '48.45', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '22.e1.a1', '33.a1.a1'], 'contains': ['132.f1.a1', '132.m1.a1', '132.m1.b1', '198.j1.a1'], 'core': '132.f1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 57212464, 19522081488], 'label': '4752.h.66.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '66.k1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331451
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '72.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '36.d1.a1', '36.e1.a1', '36.j1.a1', '36.j1.b1', '36.k1.a1', '36.k1.b1'], 'contains': ['144.a1.a1', '216.a1.a1', '792.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 24590313888, 23839464637], 'label': '4752.h.72.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1', '36.d1.a1', '36.e1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1', '792.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.14', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331452
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '72.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.h1.b1'], 'contains': ['144.b1.a1', '216.a1.a1', '792.b1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637, 19647222832], 'label': '4752.h.72.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.a1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1', '36.f1.a1', '36.g1.a1', '36.h1.b1', '36.h1.a1'], 'normal_contains': ['144.b1.a1', '216.a1.a1', '792.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.5', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331453
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.i1.a1', '36.l1.a1', '36.m1.a1'], 'contains': ['144.c1.a1', '216.a1.a1', '792.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637], 'label': '4752.h.72.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331454
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '24.f1.a1', '24.f1.b1', '36.a1.a1'], 'contains': ['144.a1.a1', '216.b1.a1', '792.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 2690543349, 24590313888], 'label': '4752.h.72.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331455
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.b1.a1'], 'contains': ['144.b1.a1', '216.b1.a1', '792.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026109, 24590313888, 19647222832], 'label': '4752.h.72.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.e1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331456
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.i1.a1'], 'contains': ['144.c1.a1', '216.b1.a1', '792.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [7883917508, 24590313888, 250283282], 'label': '4752.h.72.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.f1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331457
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.i1.a1'], 'contains': ['144.c1.a1', '216.b1.a1', '792.f1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888], 'label': '4752.h.72.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.f1.b1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331458
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '240.208', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.e1.a1', '12.h1.a1', '12.l1.a1', '44.c1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.e1.a1', '12.h1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331459
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '220.7', 'aut_weyl_index': 288, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '36.j1.a1'], 'contains': ['144.a1.a1', '216.c1.a1', '792.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16330971943, 24590313888, 158006], 'label': '4752.h.72.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '72.g1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60331460
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '220.7', 'aut_weyl_index': 288, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.h1.b1', '36.j1.b1'], 'contains': ['144.a1.a1', '216.c1.b1', '792.g1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16330971943, 8560511, 24590313888], 'label': '4752.h.72.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '72.g1.b1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60331461
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '660.15', 'aut_weyl_index': 96, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.c1.a1'], 'contains': ['144.b1.a1', '216.c1.a1', '792.h1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24590313888, 19647222832, 158006], 'label': '4752.h.72.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.h1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '66.3'}
  • id: 60331462
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '660.15', 'aut_weyl_index': 96, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '36.c1.b1'], 'contains': ['144.b1.a1', '216.c1.b1', '792.h1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [8560511, 24590313888, 19647222832], 'label': '4752.h.72.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '72.h1.b1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.b1', 'subgroup_fusion': None, 'weyl_group': '66.3'}
  • id: 60331463
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '88.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1', '44.d1.a1', '44.d1.b1', '44.e1.a1', '44.e1.b1'], 'contains': ['176.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 19522081488, 2127406644], 'label': '4752.h.88.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.a1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1'], 'normal_contains': ['176.a1.a1', '264.a1.a1', '264.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '44.4', 'quotient_action_kernel_order': 44, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331464
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.a1'], 'contains': ['176.a1.a1', '264.d1.a1', '264.e1.a1', '264.f1.a1', '264.f1.b1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 22713190600, 19522081488, 2127406644], 'label': '4752.h.88.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '88.b1.a1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331465
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1760, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.d1.a1'], 'contains': ['176.a1.a1', '264.g1.a1', '264.h1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': None, 'generators': [22650619827, 19522081488, 2127406644, 158006], 'label': '4752.h.88.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '88.c1.a1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60331466
    {'ambient': '4752.h', 'aut_centralizer_order': 40, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1760, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '44.d1.b1'], 'contains': ['176.a1.a1', '264.g1.b1', '264.h1.b1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': None, 'generators': [22650619827, 8560511, 19522081488, 2127406644], 'label': '4752.h.88.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.b1', 'old_label': '88.c1.b1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60331467
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '99.a1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1980, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '33.a1.a1', '33.b1.a1'], 'contains': ['198.a1.a1', '198.c1.a1', '198.c1.b1', '198.f1.a1', '198.f1.b1', '198.g1.a1', '198.j1.a1', '297.a1.a1'], 'core': '198.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 2189977417, 158006], 'label': '4752.h.99.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '99.a1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '99.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331468
    {'ambient': '4752.h', 'aut_centralizer_order': 60, 'aut_label': '99.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '96.209', 'aut_weyl_index': 660, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '33.b1.a1'], 'contains': ['198.b1.a1', '198.d1.a1', '198.d1.b1', '198.h1.a1', '198.h1.b1', '198.i1.a1', '198.k1.a1', '297.a1.a1'], 'core': '198.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 24778026109, 11075027061, 2127406644, 158006], 'label': '4752.h.99.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '99.b1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '99.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331469
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.f1.a1', '12.m1.a1', '44.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 23839464637, 19647222832, 57212464], 'label': '4752.h.4.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '264.38', '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': '132.9'}
  • id: 60331470
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.i1.a1', '54.a1.a1', '54.b1.a1', '54.b1.b1'], 'contains': ['216.a1.a1', '216.b1.a1', '1188.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026109, 24590313888, 23839464637], 'label': '4752.h.108.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1', '54.a1.a1'], 'normal_contains': ['216.a1.a1', '1188.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.9', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331471
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '108.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.f1.a1', '36.l1.a1', '54.a1.a1', '54.c1.a1', '54.c1.b1'], 'contains': ['216.a1.a1', '1188.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637, 7195639147], 'label': '4752.h.108.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.d1.a1', '36.f1.a1', '54.a1.a1'], 'normal_contains': ['216.a1.a1', '1188.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.9', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331472
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '108.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.g1.a1', '36.m1.a1', '54.a1.a1', '54.d1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '1188.c1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [17644958238, 24590313888, 23839464637], 'label': '4752.h.108.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.c1.a1', 'normal_contained_in': ['36.e1.a1', '36.g1.a1', '54.a1.a1'], 'normal_contains': ['216.a1.a1', '1188.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.c1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.9', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331473
    {'ambient': '4752.h', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '220.7', 'aut_weyl_index': 288, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.j1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '1188.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [24590313888, 23839464637, 158006], 'label': '4752.h.108.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331474
    {'ambient': '4752.h', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '220.7', 'aut_weyl_index': 288, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '36.j1.b1', '54.b1.b1', '54.c1.b1', '54.d1.a1'], 'contains': ['216.a1.a1', '216.c1.b1', '1188.d1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [8560511, 24590313888, 23839464637], 'label': '4752.h.108.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331475
    {'ambient': '4752.h', 'aut_centralizer_order': 48, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '220.7', 'aut_weyl_index': 288, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.k1.a1', '54.b1.a1', '54.c1.b1', '54.e1.a1'], 'contains': ['216.a1.a1', '1188.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [57355781, 24590313888, 23839464637], 'label': '4752.h.108.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331476
    {'ambient': '4752.h', 'aut_centralizer_order': 48, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '220.7', 'aut_weyl_index': 288, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.b1', '36.k1.b1', '54.b1.b1', '54.c1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '1188.e1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [24590313888, 23839464637, 23638174], 'label': '4752.h.108.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331477
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '132.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.a1.a1', '66.a1.a1', '66.d1.a1', '66.d1.b1'], 'contains': ['264.a1.a1', '264.d1.a1', '396.a1.a1', '396.b1.a1', '396.g1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 2127406644], 'label': '4752.h.132.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.a1.a1', 'normal_contained_in': ['12.a1.a1', '44.a1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1', '396.a1.a1', '396.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.4', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331478
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '132.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '44.a1.a1', '66.b1.a1', '66.c1.a1', '66.c1.b1'], 'contains': ['264.b1.a1', '264.e1.a1', '396.a1.a1'], 'core': '132.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 2189977417, 19522081488], 'label': '4752.h.132.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.b1.a1', 'normal_contained_in': ['12.b1.a1', '44.a1.a1', '66.b1.a1'], 'normal_contains': ['264.b1.a1', '396.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.b1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.4', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331479
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '132.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '44.b1.a1', '66.a1.a1', '66.h1.a1', '66.h1.b1'], 'contains': ['264.a1.a1', '396.c1.a1', '396.e1.a1', '396.l1.a1'], 'core': '132.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 20898638422, 2127406644], 'label': '4752.h.132.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.c1.a1', 'normal_contained_in': ['12.d1.a1', '44.b1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1', '396.c1.a1', '396.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.c1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.4', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331480
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '12.f1.b1', '12.m1.b1', '44.e1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [23533366, 22650619827, 13640428742, 24590313888, 23839464637, 19647222832], 'label': '4752.h.4.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '264.38', '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': '132.9'}
  • id: 60331481
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '132.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '44.c1.a1', '66.a1.a1', '66.i1.a1', '66.j1.a1'], 'contains': ['264.a1.a1', '396.d1.a1', '396.f1.a1', '396.m1.a1'], 'core': '132.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 11075027061, 2127406644], 'label': '4752.h.132.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.d1.a1', 'normal_contained_in': ['12.e1.a1', '44.c1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1', '396.d1.a1', '396.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.d1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.4', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331482
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '132.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '44.b1.a1', '66.b1.a1', '66.f1.a1', '66.f1.b1'], 'contains': ['264.b1.a1', '396.c1.a1'], 'core': '132.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 19522081488, 13765570280], 'label': '4752.h.132.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.e1.a1', 'normal_contained_in': ['12.g1.a1', '44.b1.a1', '66.b1.a1'], 'normal_contains': ['264.b1.a1', '396.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.e1.a1', 'projective_image': '132.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '132.9', 'quotient_action_kernel_order': 132, 'quotient_fusion': None, 'short_label': '132.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331483
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '132.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '44.c1.a1', '66.b1.a1', '66.g1.a1', '66.k1.a1'], 'contains': ['264.b1.a1', '396.d1.a1'], 'core': '132.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 19522081488], 'label': '4752.h.132.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.f1.a1', 'normal_contained_in': ['12.h1.a1', '44.c1.a1', '66.b1.a1'], 'normal_contains': ['264.b1.a1', '396.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.f1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '66.4', 'quotient_action_kernel_order': 66, 'quotient_fusion': None, 'short_label': '132.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331484
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '132.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '44.a1.a1', '66.e1.a1'], 'contains': ['264.c1.a1', '264.f1.a1', '264.f1.b1', '396.a1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 2127406316, 17895241274, 2189977417], 'label': '4752.h.132.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '132.g1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331485
    {'ambient': '4752.h', 'aut_centralizer_order': 80, 'aut_label': '132.h1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '44.d1.a1', '66.c1.a1', '66.f1.a1', '66.g1.a1'], 'contains': ['264.b1.a1', '264.g1.a1', '396.h1.a1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 19522081488, 158006], 'label': '4752.h.132.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '132.h1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331486
    {'ambient': '4752.h', 'aut_centralizer_order': 80, 'aut_label': '132.h1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '44.d1.b1', '66.c1.b1', '66.f1.b1', '66.g1.a1'], 'contains': ['264.b1.a1', '264.g1.b1', '396.h1.b1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 8560511, 19522081488], 'label': '4752.h.132.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '132.h1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331487
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '132.i1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '44.d1.a1', '66.d1.a1', '66.h1.a1', '66.i1.a1'], 'contains': ['264.a1.a1', '264.h1.a1', '396.h1.a1', '396.i1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 2127406644, 158006], 'label': '4752.h.132.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.i1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331488
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '132.i1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '44.d1.b1', '66.d1.b1', '66.h1.b1', '66.i1.a1'], 'contains': ['264.a1.a1', '264.h1.b1', '396.h1.b1', '396.i1.b1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 8560511, 2127406644], 'label': '4752.h.132.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.i1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331489
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '132.j1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '44.e1.a1', '66.d1.a1', '66.h1.b1', '66.j1.a1'], 'contains': ['264.a1.a1', '396.j1.a1', '396.k1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 57212464, 2127406644], 'label': '4752.h.132.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.j1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331490
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '132.j1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '44.e1.b1', '66.d1.b1', '66.h1.a1', '66.j1.a1'], 'contains': ['264.a1.a1', '396.j1.b1', '396.k1.b1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [23533366, 24778026504, 22650619827, 2127406644], 'label': '4752.h.132.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.j1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331491
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.f1.a1', '18.a1.a1', '18.g1.a1', '66.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.6.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.f1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331492
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '132.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '44.b1.a1', '66.e1.a1'], 'contains': ['264.c1.a1', '396.c1.a1'], 'core': '396.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 2127406316, 17895241274, 13765570280], 'label': '4752.h.132.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '132.k1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331493
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '132.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '44.c1.a1', '66.e1.a1'], 'contains': ['264.c1.a1', '396.d1.a1'], 'core': '396.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 17895241274], 'label': '4752.h.132.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '132.l1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331494
    {'ambient': '4752.h', 'aut_centralizer_order': 80, 'aut_label': '132.m1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '44.e1.a1', '66.c1.a1', '66.f1.b1', '66.k1.a1'], 'contains': ['264.b1.a1', '396.j1.a1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 57212464, 19522081488], 'label': '4752.h.132.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '132.m1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331495
    {'ambient': '4752.h', 'aut_centralizer_order': 80, 'aut_label': '132.m1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '44.e1.b1', '66.c1.b1', '66.f1.a1', '66.k1.a1'], 'contains': ['264.b1.a1', '396.j1.b1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [23533366, 24778026504, 2127406316, 19522081488], 'label': '4752.h.132.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '132.m1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331496
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1', '72.d1.a1', '72.g1.a1', '72.g1.b1'], 'contains': ['432.a1.a1', '1584.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 24590313888], 'label': '4752.h.144.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1', '1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '1584.621', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.36', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331497
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '144.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': ['33.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.b1.a1', '72.e1.a1', '72.h1.a1', '72.h1.b1'], 'contains': ['432.a1.a1', '1584.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 19647222832], 'label': '4752.h.144.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['48.a1.a1', '72.b1.a1'], 'normal_contains': ['432.a1.a1', '1584.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '4752.h', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.9', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331498
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 3168, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.c1.a1', '72.f1.a1', '72.f1.b1'], 'contains': ['432.a1.a1', '1584.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 24590313888], 'label': '4752.h.144.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.c1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331499
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '176.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.c1.a1', '88.c1.b1'], 'contains': ['528.a1.a1', '528.b1.a1', '528.c1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 19522081488, 2127406644], 'label': '4752.h.176.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '176.a1.a1', 'normal_contained_in': ['16.a1.a1', '88.a1.a1'], 'normal_contains': ['528.a1.a1', '528.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '528.149', 'quotient_action_image': '2.1', 'quotient_action_kernel': '88.8', 'quotient_action_kernel_order': 88, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331500
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '198.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '66.a1.a1', '66.b1.a1', '66.e1.a1', '99.a1.a1'], 'contains': ['396.a1.a1', '396.c1.a1', '396.d1.a1', '594.a1.a1'], 'core': '198.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 2189977417], 'label': '4752.h.198.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '198.a1.a1', 'normal_contained_in': ['18.b1.a1', '66.a1.a1', '66.b1.a1'], 'normal_contains': ['396.a1.a1', '396.c1.a1', '396.d1.a1', '594.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '198.a1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '99.2', 'quotient_action_kernel_order': 99, 'quotient_fusion': None, 'short_label': '198.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331501
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '198.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '2.b1.a1', 'complements': ['24.g1.a1', '24.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '66.a1.a1', '99.b1.a1'], 'contains': ['396.b1.a1', '396.e1.a1', '396.f1.a1', '594.a1.a1'], 'core': '198.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 24778026109, 11075027061, 2127406644], 'label': '4752.h.198.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '198.b1.a1', 'normal_contained_in': ['18.c1.a1', '66.a1.a1'], 'normal_contains': ['396.b1.a1', '396.e1.a1', '396.f1.a1', '594.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '198.b1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '99.1', 'quotient_action_kernel_order': 99, 'quotient_fusion': None, 'short_label': '198.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331502
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.b1', '12.f1.b1', '18.a1.b1', '18.g1.b1', '66.d1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 8560511, 19647222832, 22713190600, 22650619827, 23839464637], 'label': '4752.h.6.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.b1', '12.f1.b1', '18.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331503
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '66.c1.a1', '66.d1.a1', '99.a1.a1'], 'contains': ['396.a1.a1', '396.h1.a1', '396.j1.a1', '594.b1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 2189977417, 158006], 'label': '4752.h.198.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '198.c1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331504
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.b1', '66.c1.b1', '66.d1.b1', '99.a1.a1'], 'contains': ['396.a1.a1', '396.h1.b1', '396.j1.b1', '594.b1.b1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 8560511, 2189977417], 'label': '4752.h.198.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '198.c1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331505
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '66.d1.a1', '99.b1.a1'], 'contains': ['396.b1.a1', '396.i1.a1', '396.k1.a1', '594.b1.a1'], 'core': '396.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 24778026109, 2127406644, 158006], 'label': '4752.h.198.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331506
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '66.d1.b1', '99.b1.a1'], 'contains': ['396.b1.a1', '396.i1.b1', '396.k1.b1', '594.b1.b1'], 'core': '396.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 24778026109, 8560511, 2127406644], 'label': '4752.h.198.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331507
    {'ambient': '4752.h', 'aut_centralizer_order': 3960, 'aut_label': '198.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '66.a1.a1'], 'contains': ['396.g1.a1', '396.l1.a1', '396.m1.a1', '594.a1.a1'], 'core': '594.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 22650619827, 3941959033, 22713190600], 'label': '4752.h.198.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '66.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '198.e1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331508
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.f1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '66.f1.a1', '66.h1.a1', '99.a1.a1'], 'contains': ['396.c1.a1', '396.h1.a1', '396.j1.b1', '594.c1.a1'], 'core': '396.c1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 13765570280, 158006], 'label': '4752.h.198.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '198.f1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331509
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.f1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7920, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.b1', '66.f1.b1', '66.h1.b1', '99.a1.a1'], 'contains': ['396.c1.a1', '396.h1.b1', '396.j1.a1', '594.c1.b1'], 'core': '396.c1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 57212464, 27992073], 'label': '4752.h.198.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '198.f1.b1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331510
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.g1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 3960, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '66.g1.a1', '66.i1.a1', '99.a1.a1'], 'contains': ['396.d1.a1', '396.h1.a1', '396.h1.b1', '594.d1.a1'], 'core': '396.d1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 158006], 'label': '4752.h.198.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '198.g1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331511
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.h1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '66.h1.a1', '99.b1.a1'], 'contains': ['396.e1.a1', '396.i1.a1', '396.k1.b1', '594.c1.a1'], 'core': '396.e1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 2127406644, 13765570300, 158006], 'label': '4752.h.198.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.h1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331512
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.h1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2640, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '66.h1.b1', '99.b1.a1'], 'contains': ['396.e1.a1', '396.i1.b1', '396.k1.a1', '594.c1.b1'], 'core': '396.e1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 57355781, 2127406644, 27992073], 'label': '4752.h.198.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.h1.b1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331513
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '132.e1.a1', 'complements': ['2376.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '6.a1.a1', '6.g1.a1', '22.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 22713190600, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.2.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331514
    {'ambient': '4752.h', 'aut_centralizer_order': 396, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.238', 'aut_weyl_index': 396, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '18.b1.a1', '18.c1.a1', '18.h1.a1', '66.a1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.6.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '18.b1.a1', '18.c1.a1', '66.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331515
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.i1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '66.i1.a1', '99.b1.a1'], 'contains': ['396.f1.a1', '396.i1.a1', '396.i1.b1', '594.d1.a1'], 'core': '396.f1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 11075027061, 2127406644, 158006], 'label': '4752.h.198.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331516
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.j1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 3960, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '66.j1.a1', '66.k1.a1', '99.a1.a1'], 'contains': ['396.d1.a1', '396.j1.a1', '396.j1.b1', '594.e1.a1'], 'core': '396.d1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 57212464], 'label': '4752.h.198.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '198.j1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331517
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '198.k1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1320, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '66.j1.a1', '99.b1.a1'], 'contains': ['396.f1.a1', '396.k1.a1', '396.k1.b1', '594.e1.a1'], 'core': '396.f1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 57355781, 11075027061, 2127406644], 'label': '4752.h.198.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '198.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '198.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331518
    {'ambient': '4752.h', 'aut_centralizer_order': 6336, 'aut_label': '216.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 6336, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.d1.b1', '108.e1.a1', '108.e1.b1'], 'contains': ['432.a1.a1', '2376.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637], 'label': '4752.h.216.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '72.b1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'normal_contains': ['432.a1.a1', '2376.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.29', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331519
    {'ambient': '4752.h', 'aut_centralizer_order': 3168, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 6336, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.e1.a1', '72.f1.a1', '72.f1.b1', '108.a1.a1'], 'contains': ['432.a1.a1', '2376.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026109, 24590313888], 'label': '4752.h.216.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '216.b1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331520
    {'ambient': '4752.h', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 576, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.h1.a1', '108.d1.a1'], 'contains': ['432.a1.a1', '2376.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [24590313888, 158006], 'label': '4752.h.216.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '216.c1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60331521
    {'ambient': '4752.h', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '110.1', 'aut_weyl_index': 576, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.b1', '72.h1.b1', '108.d1.b1'], 'contains': ['432.a1.a1', '2376.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [8560511, 24590313888], 'label': '4752.h.216.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '216.c1.b1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60331522
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '264.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1', '132.c1.a1', '132.d1.a1', '132.i1.a1', '132.i1.b1', '132.j1.a1', '132.j1.b1'], 'contains': ['528.a1.a1', '792.a1.a1', '792.b1.a1', '792.c1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 2127406644], 'label': '4752.h.264.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '264.a1.a1', 'normal_contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1', '132.c1.a1', '132.d1.a1'], 'normal_contains': ['528.a1.a1', '792.a1.a1', '792.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '132.10', 'quotient_action_kernel_order': 132, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331523
    {'ambient': '4752.h', 'aut_centralizer_order': 10560, 'aut_label': '264.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.a1.a1', '132.b1.a1', '132.e1.a1', '132.f1.a1', '132.h1.a1', '132.h1.b1', '132.m1.a1', '132.m1.b1'], 'contains': ['528.b1.a1', '792.a1.a1'], 'core': '264.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 19522081488], 'label': '4752.h.264.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '264.b1.a1', 'normal_contained_in': ['24.b1.a1', '88.a1.a1', '132.b1.a1', '132.e1.a1', '132.f1.a1'], 'normal_contains': ['528.b1.a1', '792.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.b1.a1', 'projective_image': '264.38', 'quotient_action_image': '1.1', 'quotient_action_kernel': '264.38', 'quotient_action_kernel_order': 264, 'quotient_fusion': None, 'short_label': '264.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331524
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.a1.a1', '132.g1.a1', '132.k1.a1', '132.l1.a1'], 'contains': ['528.c1.a1', '792.a1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 2127406316, 17895241274], 'label': '4752.h.264.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '88.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.c1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331525
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '240.208', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': ['792.h1.a1', '792.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.g1.a1', '12.h1.a1', '18.b1.a1', '66.b1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 17644958238, 2690543349, 13640428742, 24590313888, 23839464637], 'label': '4752.h.6.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.b1.a1', '12.g1.a1', '12.h1.a1', '18.b1.a1', '66.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331526
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '264.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '88.b1.a1', '132.a1.a1'], 'contains': ['528.a1.a1', '792.d1.a1', '792.e1.a1', '792.f1.a1', '792.f1.b1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 22713190600, 2127406644], 'label': '4752.h.264.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.d1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331527
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '264.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '88.b1.a1', '132.b1.a1'], 'contains': ['528.b1.a1', '792.d1.a1'], 'core': '528.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2127406316, 2189977417, 19522081488], 'label': '4752.h.264.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.e1.a1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331528
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '264.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '88.b1.a1', '132.g1.a1'], 'contains': ['528.c1.a1', '792.d1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2127406316, 2189977417, 12263871794], 'label': '4752.h.264.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.f1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331529
    {'ambient': '4752.h', 'aut_centralizer_order': 2640, 'aut_label': '264.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '88.b1.a1', '132.g1.a1'], 'contains': ['528.c1.a1', '792.d1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2127406316, 17895241274, 2189977417], 'label': '4752.h.264.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.f1.b1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331530
    {'ambient': '4752.h', 'aut_centralizer_order': 80, 'aut_label': '264.g1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '88.c1.a1', '132.h1.a1'], 'contains': ['528.b1.a1', '792.g1.a1'], 'core': '528.b1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': None, 'generators': [2127406316, 19522081488, 158006], 'label': '4752.h.264.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.f1.a1', 'old_label': '264.g1.a1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331531
    {'ambient': '4752.h', 'aut_centralizer_order': 80, 'aut_label': '264.g1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '88.c1.b1', '132.h1.b1'], 'contains': ['528.b1.a1', '792.g1.b1'], 'core': '528.b1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': None, 'generators': [2127406316, 8560511, 19522081488], 'label': '4752.h.264.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.f1.b1', 'old_label': '264.g1.b1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331532
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '264.h1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5280, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '88.c1.a1', '132.i1.a1'], 'contains': ['528.a1.a1', '792.g1.a1', '792.h1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': None, 'generators': [22650619827, 2127406644, 158006], 'label': '4752.h.264.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '264.h1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60331533
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '264.h1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5280, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '88.c1.b1', '132.i1.b1'], 'contains': ['528.a1.a1', '792.g1.b1', '792.h1.b1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': None, 'generators': [22650619827, 8560511, 2127406644], 'label': '4752.h.264.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.b1', 'old_label': '264.h1.b1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60331534
    {'ambient': '4752.h', 'aut_centralizer_order': 120, 'aut_label': '297.a1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '16.11', 'aut_weyl_index': 3960, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '99.a1.a1', '99.b1.a1'], 'contains': ['594.a1.a1', '594.b1.a1', '594.b1.b1', '594.c1.a1', '594.c1.b1', '594.d1.a1', '594.e1.a1'], 'core': '594.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 3941959033, 24778026109, 158006], 'label': '4752.h.297.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '297.a1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '297.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331535
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '396.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '132.a1.a1', '132.b1.a1', '132.g1.a1', '198.a1.a1', '198.c1.a1', '198.c1.b1'], 'contains': ['792.a1.a1', '792.d1.a1', '1188.a1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 2189977417], 'label': '4752.h.396.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.a1.a1', 'normal_contained_in': ['36.a1.a1', '132.a1.a1', '132.b1.a1', '198.a1.a1'], 'normal_contains': ['792.a1.a1', '1188.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.10', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331536
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '12.f1.b1', '18.d1.a1', '18.i1.a1', '66.h1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9323045302, 22650619827, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.6.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.d1.a1', '12.f1.b1', '18.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331537
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '396.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '132.a1.a1', '198.b1.a1', '198.d1.a1', '198.d1.b1'], 'contains': ['792.b1.a1', '792.e1.a1', '1188.a1.a1'], 'core': '396.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 24778026109, 2127406644], 'label': '4752.h.396.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.b1.a1', 'normal_contained_in': ['36.b1.a1', '132.a1.a1', '198.b1.a1'], 'normal_contains': ['792.b1.a1', '1188.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.b1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.4', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331538
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '396.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '132.c1.a1', '132.e1.a1', '132.k1.a1', '198.a1.a1', '198.f1.a1', '198.f1.b1'], 'contains': ['792.a1.a1', '1188.b1.a1'], 'core': '396.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 13765570280], 'label': '4752.h.396.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.c1.a1', 'normal_contained_in': ['36.d1.a1', '132.c1.a1', '132.e1.a1', '198.a1.a1'], 'normal_contains': ['792.a1.a1', '1188.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.c1.a1', 'projective_image': '396.27', 'quotient_action_image': '1.1', 'quotient_action_kernel': '396.27', 'quotient_action_kernel_order': 396, 'quotient_fusion': None, 'short_label': '396.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331539
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '396.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '132.d1.a1', '132.f1.a1', '132.l1.a1', '198.a1.a1', '198.g1.a1', '198.j1.a1'], 'contains': ['792.a1.a1', '1188.c1.a1'], 'core': '396.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033], 'label': '4752.h.396.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.d1.a1', 'normal_contained_in': ['36.e1.a1', '132.d1.a1', '132.f1.a1', '198.a1.a1'], 'normal_contains': ['792.a1.a1', '1188.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.d1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.10', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331596
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.g1.a1', '12.j1.a1', '12.m1.b1', '18.i1.a1', '66.f1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888, 13515287295, 23839464637, 158006], 'label': '4752.h.6.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331540
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '396.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '132.c1.a1', '198.b1.a1', '198.h1.a1', '198.h1.b1'], 'contains': ['792.b1.a1', '1188.b1.a1'], 'core': '396.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406644, 13765570300], 'label': '4752.h.396.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.e1.a1', 'normal_contained_in': ['36.f1.a1', '132.c1.a1', '198.b1.a1'], 'normal_contains': ['792.b1.a1', '1188.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.e1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.4', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331541
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '396.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '132.d1.a1', '198.b1.a1', '198.i1.a1', '198.k1.a1'], 'contains': ['792.b1.a1', '1188.c1.a1'], 'core': '396.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 11075027061, 2127406644], 'label': '4752.h.396.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.f1.a1', 'normal_contained_in': ['36.g1.a1', '132.d1.a1', '198.b1.a1'], 'normal_contains': ['792.b1.a1', '1188.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.f1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.4', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331542
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '396.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '132.a1.a1', '198.e1.a1'], 'contains': ['792.c1.a1', '792.f1.a1', '792.f1.b1', '1188.a1.a1'], 'core': '1188.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600], 'label': '4752.h.396.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '396.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331543
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.h1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '132.h1.a1', '132.i1.a1', '198.c1.a1', '198.f1.a1', '198.g1.a1'], 'contains': ['792.a1.a1', '792.g1.a1', '1188.d1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 158006], 'label': '4752.h.396.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '396.h1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331544
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.h1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.b1', '132.h1.b1', '132.i1.b1', '198.c1.b1', '198.f1.b1', '198.g1.a1'], 'contains': ['792.a1.a1', '792.g1.b1', '1188.d1.b1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 8560511], 'label': '4752.h.396.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '396.h1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331545
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.i1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5280, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '132.i1.a1', '198.d1.a1', '198.h1.a1', '198.i1.a1'], 'contains': ['792.b1.a1', '792.h1.a1', '1188.d1.a1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 2127406644, 158006], 'label': '4752.h.396.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '396.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331546
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.i1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5280, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '132.i1.b1', '198.d1.b1', '198.h1.b1', '198.i1.a1'], 'contains': ['792.b1.a1', '792.h1.b1', '1188.d1.b1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 8560511, 2127406644], 'label': '4752.h.396.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '396.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331547
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.c1.b1', '12.d1.a1', '12.f1.a1', '18.d1.b1', '18.i1.b1', '66.h1.b1'], 'core': '6.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 8560511, 24590313888, 23839464637, 19647222832, 57212464], 'label': '4752.h.6.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.b1', 'normal_contained_in': ['2.c1.b1', '3.a1.a1'], 'normal_contains': ['12.c1.b1', '12.d1.a1', '12.f1.a1', '18.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331548
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.j1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '132.j1.a1', '132.m1.a1', '198.c1.a1', '198.f1.b1', '198.j1.a1'], 'contains': ['792.a1.a1', '1188.e1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 57212464], 'label': '4752.h.396.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '396.j1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331549
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.j1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.b1', '132.j1.b1', '132.m1.b1', '198.c1.b1', '198.f1.a1', '198.j1.a1'], 'contains': ['792.a1.a1', '1188.e1.b1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [23533366, 24778026504, 2127406316], 'label': '4752.h.396.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '396.j1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331550
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.k1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5280, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '132.j1.a1', '198.d1.a1', '198.h1.b1', '198.k1.a1'], 'contains': ['792.b1.a1', '1188.e1.a1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 57355781, 2127406644], 'label': '4752.h.396.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '396.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331551
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '396.k1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5280, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.b1', '132.j1.b1', '198.d1.b1', '198.h1.a1', '198.k1.a1'], 'contains': ['792.b1.a1', '1188.e1.b1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 23638174, 2127406644], 'label': '4752.h.396.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '396.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.k1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331552
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '396.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '132.c1.a1', '198.e1.a1'], 'contains': ['792.c1.a1', '1188.b1.a1'], 'core': '1188.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 20898638422, 62571135], 'label': '4752.h.396.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '396.l1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331553
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '396.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1.a1', '132.d1.a1', '198.e1.a1'], 'contains': ['792.c1.a1', '1188.c1.a1'], 'core': '1188.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 22650619827, 3941959033], 'label': '4752.h.396.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '396.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '396.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331554
    {'ambient': '4752.h', 'aut_centralizer_order': 6336, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 6336, 'centralizer': '2.b1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1', '216.c1.b1'], 'contains': ['4752.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888], 'label': '4752.h.432.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.a1.a1', '144.b1.a1', '216.a1.a1'], 'normal_contains': ['4752.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '4752.h', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.73', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331555
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '528.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1', '264.d1.a1', '264.h1.a1', '264.h1.b1'], 'contains': ['1584.a1.a1', '1584.b1.a1', '1584.c1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 2127406644], 'label': '4752.h.528.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '528.a1.a1', 'normal_contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1'], 'normal_contains': ['1584.a1.a1', '1584.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '528.a1.a1', 'projective_image': '1584.621', 'quotient_action_image': '2.1', 'quotient_action_kernel': '264.28', 'quotient_action_kernel_order': 264, 'quotient_fusion': None, 'short_label': '528.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331556
    {'ambient': '4752.h', 'aut_centralizer_order': 10560, 'aut_label': '528.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '1.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '176.a1.a1', '264.b1.a1', '264.e1.a1', '264.g1.a1', '264.g1.b1'], 'contains': ['1584.a1.a1'], 'core': '528.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2127406316, 19522081488], 'label': '4752.h.528.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '528.b1.a1', 'normal_contained_in': ['48.b1.a1', '176.a1.a1', '264.b1.a1'], 'normal_contains': ['1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '528.b1.a1', 'projective_image': '528.149', 'quotient_action_image': '1.1', 'quotient_action_kernel': '528.149', 'quotient_action_kernel_order': 528, 'quotient_fusion': None, 'short_label': '528.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331557
    {'ambient': '4752.h', 'aut_centralizer_order': 5280, 'aut_label': '528.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10560, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '176.a1.a1', '264.c1.a1', '264.f1.a1', '264.f1.b1'], 'contains': ['1584.a1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2127406316, 17895241274], 'label': '4752.h.528.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '176.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '528.c1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331558
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.c1.b1', '12.e1.a1', '18.e1.a1', '18.j1.a1', '66.i1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637, 19647222832, 3378821867, 158006], 'label': '4752.h.6.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.c1.b1', '12.e1.a1', '18.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331559
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '594.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '2.b1.a1', 'complements': ['8.c1.a1', '8.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '198.a1.a1', '198.b1.a1', '198.e1.a1', '297.a1.a1'], 'contains': ['1188.a1.a1', '1188.b1.a1', '1188.c1.a1'], 'core': '594.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 3941959033, 24778026109], 'label': '4752.h.594.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '594.a1.a1', 'normal_contained_in': ['54.a1.a1', '198.a1.a1', '198.b1.a1'], 'normal_contains': ['1188.a1.a1', '1188.b1.a1', '1188.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '594.a1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '297.2', 'quotient_action_kernel_order': 297, 'quotient_fusion': None, 'short_label': '594.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331560
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '594.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '198.c1.a1', '198.d1.a1', '297.a1.a1'], 'contains': ['1188.a1.a1', '1188.d1.a1', '1188.e1.a1'], 'core': '1188.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 24778026109, 158006], 'label': '4752.h.594.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '594.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '594.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331561
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '594.b1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.b1', '198.c1.b1', '198.d1.b1', '297.a1.a1'], 'contains': ['1188.a1.a1', '1188.d1.b1', '1188.e1.b1'], 'core': '1188.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 24778026109, 8560511], 'label': '4752.h.594.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '594.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '594.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331562
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '594.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '198.f1.a1', '198.h1.a1', '297.a1.a1'], 'contains': ['1188.b1.a1', '1188.d1.a1', '1188.e1.b1'], 'core': '1188.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 20898638516, 158006], 'label': '4752.h.594.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '594.c1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '594.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331563
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '594.c1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15840, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.b1', '198.f1.b1', '198.h1.b1', '297.a1.a1'], 'contains': ['1188.b1.a1', '1188.d1.b1', '1188.e1.a1'], 'core': '1188.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24831953, 24778026504, 57355781], 'label': '4752.h.594.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '594.c1.b1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '594.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331564
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '594.d1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 7920, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '198.g1.a1', '198.i1.a1', '297.a1.a1'], 'contains': ['1188.c1.a1', '1188.d1.a1', '1188.d1.b1'], 'core': '1188.c1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 3941959033, 158006], 'label': '4752.h.594.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '594.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '594.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331565
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '594.e1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '8.3', 'aut_weyl_index': 7920, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '198.j1.a1', '198.k1.a1', '297.a1.a1'], 'contains': ['1188.c1.a1', '1188.e1.a1', '1188.e1.b1'], 'core': '1188.c1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 57355781, 3941959033], 'label': '4752.h.594.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '594.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '594.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331566
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '792.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1', '396.a1.a1', '396.c1.a1', '396.d1.a1', '396.h1.a1', '396.h1.b1', '396.j1.a1', '396.j1.b1'], 'contains': ['1584.a1.a1', '2376.a1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406316], 'label': '4752.h.792.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '792.a1.a1', 'normal_contained_in': ['72.a1.a1', '264.a1.a1', '264.b1.a1', '396.a1.a1', '396.c1.a1', '396.d1.a1'], 'normal_contains': ['1584.a1.a1', '2376.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '792.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '1.1', 'quotient_action_kernel': '792.134', 'quotient_action_kernel_order': 792, 'quotient_fusion': None, 'short_label': '792.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331567
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '792.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '264.a1.a1', '396.b1.a1', '396.e1.a1', '396.f1.a1', '396.i1.a1', '396.i1.b1', '396.k1.a1', '396.k1.b1'], 'contains': ['1584.b1.a1', '2376.a1.a1'], 'core': '792.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 2127406644], 'label': '4752.h.792.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '792.b1.a1', 'normal_contained_in': ['72.b1.a1', '264.a1.a1', '396.b1.a1', '396.e1.a1', '396.f1.a1'], 'normal_contains': ['1584.b1.a1', '2376.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '792.b1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '396.10', 'quotient_action_kernel_order': 396, 'quotient_fusion': None, 'short_label': '792.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331568
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '792.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '264.a1.a1', '396.g1.a1', '396.l1.a1', '396.m1.a1'], 'contains': ['1584.c1.a1', '2376.a1.a1'], 'core': '2376.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026504, 22650619827], 'label': '4752.h.792.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '264.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331569
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '12.f1.b1', '18.f1.a1', '18.k1.a1', '66.j1.a1'], 'core': '6.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637, 19647222832, 57212464, 3378821867], 'label': '4752.h.6.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.f1.a1', 'normal_contained_in': ['2.e1.a1', '3.a1.a1'], 'normal_contains': ['12.e1.a1', '12.f1.b1', '12.f1.a1', '18.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331570
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '792.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '264.d1.a1', '264.e1.a1', '264.f1.a1', '264.f1.b1', '396.a1.a1'], 'contains': ['1584.a1.a1', '2376.b1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2127406316, 2189977417], 'label': '4752.h.792.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.d1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331571
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '792.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '264.d1.a1', '396.b1.a1'], 'contains': ['1584.b1.a1', '2376.b1.a1'], 'core': '1584.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026109, 2127406644], 'label': '4752.h.792.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '396.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.e1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331572
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '792.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '264.d1.a1', '396.g1.a1'], 'contains': ['1584.c1.a1', '2376.b1.a1'], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [62571135, 24778026142], 'label': '4752.h.792.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.f1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331573
    {'ambient': '4752.h', 'aut_centralizer_order': 7920, 'aut_label': '792.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.b1', '264.d1.a1', '396.g1.a1'], 'contains': ['1584.c1.a1', '2376.b1.a1'], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 22713190600], 'label': '4752.h.792.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '132.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '792.f1.b1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331574
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '792.g1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '264.g1.a1', '264.h1.a1', '396.h1.a1'], 'contains': ['1584.a1.a1', '2376.c1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': None, 'generators': [2127406316, 158006], 'label': '4752.h.792.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.f1.a1', 'old_label': '792.g1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331575
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '792.g1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.b1', '264.g1.b1', '264.h1.b1', '396.h1.b1'], 'contains': ['1584.a1.a1', '2376.c1.b1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': None, 'generators': [2127406316, 8560511], 'label': '4752.h.792.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.f1.b1', 'old_label': '792.g1.b1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331576
    {'ambient': '4752.h', 'aut_centralizer_order': 240, 'aut_label': '792.h1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10560, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '264.h1.a1', '396.i1.a1'], 'contains': ['1584.b1.a1', '2376.c1.a1'], 'core': '1584.b1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': None, 'generators': [2127406644, 158006], 'label': '4752.h.792.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.c1.a1', 'old_label': '792.h1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 60331578
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '1188.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '396.a1.a1', '396.b1.a1', '396.g1.a1', '594.a1.a1', '594.b1.a1', '594.b1.b1'], 'contains': ['2376.a1.a1', '2376.b1.a1'], 'core': '1188.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 24778026109], 'label': '4752.h.1188.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1188.a1.a1', 'normal_contained_in': ['108.a1.a1', '396.a1.a1', '396.b1.a1', '594.a1.a1'], 'normal_contains': ['2376.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1188.a1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '594.20', 'quotient_action_kernel_order': 594, 'quotient_fusion': None, 'short_label': '1188.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331579
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '1188.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '396.c1.a1', '396.e1.a1', '396.l1.a1', '594.a1.a1', '594.c1.a1', '594.c1.b1'], 'contains': ['2376.a1.a1'], 'core': '1188.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 20898638516], 'label': '4752.h.1188.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1188.b1.a1', 'normal_contained_in': ['108.b1.a1', '396.c1.a1', '396.e1.a1', '594.a1.a1'], 'normal_contains': ['2376.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1188.b1.a1', 'projective_image': '1188.57', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1188.57', 'quotient_action_kernel_order': 1188, 'quotient_fusion': None, 'short_label': '1188.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331580
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.j1.a1', '12.m1.a1', '18.g1.a1', '66.c1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 2690543349, 13640428742, 24590313888, 23839464637, 158006], 'label': '4752.h.6.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331581
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '1188.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '396.d1.a1', '396.f1.a1', '396.m1.a1', '594.a1.a1', '594.d1.a1', '594.e1.a1'], 'contains': ['2376.a1.a1'], 'core': '1188.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 3941959033], 'label': '4752.h.1188.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1188.c1.a1', 'normal_contained_in': ['108.c1.a1', '396.d1.a1', '396.f1.a1', '594.a1.a1'], 'normal_contains': ['2376.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1188.c1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '594.20', 'quotient_action_kernel_order': 594, 'quotient_fusion': None, 'short_label': '1188.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331582
    {'ambient': '4752.h', 'aut_centralizer_order': 480, 'aut_label': '1188.d1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '396.h1.a1', '396.i1.a1', '594.b1.a1', '594.c1.a1', '594.d1.a1'], 'contains': ['2376.a1.a1', '2376.c1.a1'], 'core': '2376.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 158006], 'label': '4752.h.1188.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '1188.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1188.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331583
    {'ambient': '4752.h', 'aut_centralizer_order': 480, 'aut_label': '1188.d1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.b1', '396.h1.b1', '396.i1.b1', '594.b1.b1', '594.c1.b1', '594.d1.a1'], 'contains': ['2376.a1.a1', '2376.c1.b1'], 'core': '2376.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 8560511], 'label': '4752.h.1188.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '1188.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1188.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331584
    {'ambient': '4752.h', 'aut_centralizer_order': 480, 'aut_label': '1188.e1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '396.j1.a1', '396.k1.a1', '594.b1.a1', '594.c1.b1', '594.e1.a1'], 'contains': ['2376.a1.a1'], 'core': '2376.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 57355781], 'label': '4752.h.1188.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '1188.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1188.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331585
    {'ambient': '4752.h', 'aut_centralizer_order': 480, 'aut_label': '1188.e1', 'aut_quo_index': None, 'aut_stab_index': 66, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.b1', '396.j1.b1', '396.k1.b1', '594.b1.b1', '594.c1.a1', '594.e1.a1'], 'contains': ['2376.a1.a1'], 'core': '2376.a1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 23638174], 'label': '4752.h.1188.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '1188.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1188.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331586
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '1584.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '528.a1.a1', '528.b1.a1', '528.c1.a1', '792.a1.a1', '792.d1.a1', '792.g1.a1', '792.g1.b1'], 'contains': ['4752.a1.a1'], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2127406316], 'label': '4752.h.1584.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1584.a1.a1', 'normal_contained_in': ['144.a1.a1', '528.a1.a1', '528.b1.a1', '792.a1.a1'], 'normal_contains': ['4752.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1584.a1.a1', 'projective_image': '1584.621', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1584.621', 'quotient_action_kernel_order': 1584, 'quotient_fusion': None, 'short_label': '1584.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331587
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '1584.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': ['3.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '528.a1.a1', '792.b1.a1', '792.e1.a1', '792.h1.a1', '792.h1.b1'], 'contains': ['4752.a1.a1'], 'core': '1584.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2127406644], 'label': '4752.h.1584.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1584.b1.a1', 'normal_contained_in': ['144.b1.a1', '528.a1.a1', '792.b1.a1'], 'normal_contains': ['4752.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1584.b1.a1', 'projective_image': '4752.h', 'quotient_action_image': '2.1', 'quotient_action_kernel': '792.28', 'quotient_action_kernel_order': 792, 'quotient_fusion': None, 'short_label': '1584.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331588
    {'ambient': '4752.h', 'aut_centralizer_order': 15840, 'aut_label': '1584.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31680, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '528.a1.a1', '792.c1.a1', '792.f1.a1', '792.f1.b1'], 'contains': ['4752.a1.a1'], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827], 'label': '4752.h.1584.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '528.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '1584.c1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1584.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331589
    {'ambient': '4752.h', 'aut_centralizer_order': 63360, 'aut_label': '2376.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 63360, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '792.a1.a1', '792.b1.a1', '792.c1.a1', '1188.a1.a1', '1188.b1.a1', '1188.c1.a1', '1188.d1.a1', '1188.d1.b1', '1188.e1.a1', '1188.e1.b1'], 'contains': ['4752.a1.a1'], 'core': '2376.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504], 'label': '4752.h.2376.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2376.a1.a1', 'normal_contained_in': ['216.a1.a1', '792.a1.a1', '792.b1.a1', '1188.a1.a1', '1188.b1.a1', '1188.c1.a1'], 'normal_contains': ['4752.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2376.a1.a1', 'projective_image': None, 'quotient_action_image': '1.1', 'quotient_action_kernel': None, 'quotient_action_kernel_order': 2376, 'quotient_fusion': None, 'short_label': '2376.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331590
    {'ambient': '4752.h', 'aut_centralizer_order': 31680, 'aut_label': '2376.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 63360, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '792.d1.a1', '792.e1.a1', '792.f1.a1', '792.f1.b1', '1188.a1.a1'], 'contains': ['4752.a1.a1'], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [24778026109], 'label': '4752.h.2376.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1188.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '2376.b1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2376.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331591
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.j1.b1', '12.m1.b1', '18.g1.b1', '66.c1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 2690543349, 13640428742, 8560511, 24590313888, 23839464637], 'label': '4752.h.6.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.g1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331592
    {'ambient': '4752.h', 'aut_centralizer_order': 480, 'aut_label': '2376.c1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '1.1', 'aut_weyl_index': 63360, 'centralizer': '66.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '792.g1.a1', '792.h1.a1', '1188.d1.a1'], 'contains': ['4752.a1.a1'], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': None, 'generators': [158006], 'label': '4752.h.2376.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.f1.a1', 'old_label': '2376.c1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2376.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331593
    {'ambient': '4752.h', 'aut_centralizer_order': 480, 'aut_label': '2376.c1', 'aut_quo_index': None, 'aut_stab_index': 132, 'aut_weyl_group': '1.1', 'aut_weyl_index': 63360, 'centralizer': '66.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.b1', '792.g1.b1', '792.h1.b1', '1188.d1.b1'], 'contains': ['4752.a1.a1'], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 66, 'diagramx': None, 'generators': [8560511], 'label': '4752.h.2376.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.f1.b1', 'old_label': '2376.c1.b1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2376.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331594
    {'ambient': '4752.h', 'aut_centralizer_order': None, 'aut_label': '4752.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': ['432.a1.a1', '1584.a1.a1', '1584.b1.a1', '1584.c1.a1', '2376.a1.a1', '2376.b1.a1', '2376.c1.a1', '2376.c1.b1'], 'contains': [], 'core': '4752.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '4752.h.4752.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4752.a1.a1', 'normal_contained_in': ['432.a1.a1', '1584.a1.a1', '1584.b1.a1', '2376.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '4752.a1.a1', 'projective_image': '4752.h', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4752.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331595
    {'ambient': '4752.h', 'aut_centralizer_order': 132, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '240.208', 'aut_weyl_index': 264, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.i1.a1', '12.k1.a1', '12.l1.a1', '18.b1.a1', '66.e1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 17644958238, 2690543349, 10511889933, 24590313888, 23839464637], 'label': '4752.h.6.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '6.h1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331597
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '132.e1.a1', 'complements': ['2376.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '4.e1.b1', '6.a1.b1', '6.g1.b1', '22.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 8560511, 19647222832, 22713190600, 22650619827, 23839464637, 13640428742], 'label': '4752.h.2.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.e1.b1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331598
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.b1.a1'], 'contains': ['12.g1.a1', '12.j1.b1', '12.m1.a1', '18.i1.b1', '66.f1.b1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 13640428742, 8560511, 24590313888, 23839464637, 57212464], 'label': '4752.h.6.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.b1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331599
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.h1.a1', '12.j1.a1', '12.j1.b1', '18.j1.a1', '66.g1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 17644958238, 13640428742, 24590313888, 23839464637, 158006], 'label': '4752.h.6.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.j1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331600
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.h1.a1', '12.m1.a1', '12.m1.b1', '18.k1.a1', '66.k1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 17644958238, 13640428742, 24590313888, 23839464637, 57212464], 'label': '4752.h.6.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.k1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331601
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '88.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 23839464637, 19647222832], 'label': '4752.h.8.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.d1.a1', '4.e1.b1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331602
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.f1.b1', '88.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 13640428742, 22713190600, 24590313888, 19647222832], 'label': '4752.h.8.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '528.149', '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': '1.1'}
  • id: 60331603
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '24.g1.a1', '24.h1.a1', '88.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 19647222832, 158006], 'label': '4752.h.8.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '528.149', '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': '66.3'}
  • id: 60331604
    {'ambient': '4752.h', 'aut_centralizer_order': 4, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.a1.a1', '24.g1.b1', '24.h1.b1', '88.c1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 13640428742, 8560511, 24590313888, 19647222832], 'label': '4752.h.8.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.c1.b1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '66.3'}
  • id: 60331605
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '132.e1.a1', 'complements': ['528.b1.a1', '528.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.c1.a1', '18.d1.a1', '18.d1.b1', '18.e1.a1', '18.f1.a1', '27.a1.a1', '99.b1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026109, 24590313888, 23839464637, 19647222832, 3378821867, 158006], 'label': '4752.h.9.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.a1.a1', '18.a1.b1', '18.c1.a1', '18.d1.a1', '18.d1.b1', '18.e1.a1', '18.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '1188.57', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331606
    {'ambient': '4752.h', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.b1.a1', '18.g1.a1', '18.g1.b1', '18.i1.a1', '18.i1.b1', '18.j1.a1', '18.k1.a1', '27.a1.a1', '99.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 17644958238, 2690543349, 24590313888, 23839464637, 158006], 'label': '4752.h.9.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331607
    {'ambient': '4752.h', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '576.8609', 'aut_weyl_index': 110, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.b1.b1', '22.c1.a1', '22.c1.b1', '22.d1.a1', '22.e1.a1', '33.a1.a1', '33.b1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 11075027061, 19522081488, 2127406644, 158006], 'label': '4752.h.11.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331608
    {'ambient': '4752.h', 'aut_centralizer_order': 132, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '480.1213', 'aut_weyl_index': 132, 'centralizer': '2.b1.a1', 'complements': ['2376.c1.a1', '2376.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '6.b1.a1', '6.c1.a1', '6.h1.a1', '22.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 22713190600, 24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '6.b1.a1', '6.c1.a1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331609
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '12.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 792, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '36.a1.a1', '36.b1.a1', '36.i1.a1', '132.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888, 23839464637, 19647222832], 'label': '4752.h.12.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331610
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.a1', '6.g1.a1', '6.g1.b1'], 'contains': ['24.b1.a1', '24.e1.a1', '36.a1.a1', '132.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 2690543349, 13640428742, 24590313888, 23839464637], 'label': '4752.h.12.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1', '132.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331611
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '36.c1.a1', '36.j1.a1', '132.i1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.12.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'normal_contains': ['24.a1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331612
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.b1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.h1.b1', '36.c1.b1', '36.j1.b1', '132.i1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 8560511, 24590313888, 23839464637, 19647222832], 'label': '4752.h.12.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.b1', '6.d1.b1', '6.e1.a1'], 'normal_contains': ['24.a1.a1', '36.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331646
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '144.195', 'aut_weyl_index': 440, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.d1.a1', '44.e1.a1', '66.c1.a1', '66.d1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 19522081488, 2127406644, 158006], 'label': '4752.h.22.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331613
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '12.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 792, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '36.d1.a1', '36.f1.a1', '36.l1.a1', '132.c1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9323045302, 22650619827, 24590313888, 23839464637, 19647222832], 'label': '4752.h.12.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.d1.b1'], 'normal_contains': ['24.a1.a1', '36.d1.a1', '36.f1.a1', '132.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331614
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '12.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 792, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.e1.a1', '36.g1.a1', '36.m1.a1', '132.d1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.12.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.d1.a1', '6.b1.a1', '6.e1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '36.e1.a1', '36.g1.a1', '132.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331615
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1', '6.d1.b1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.h1.a1', '36.k1.a1', '132.j1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637, 19647222832, 57212464], 'label': '4752.h.12.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1', '6.d1.b1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '36.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331616
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.a1.b1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.h1.b1', '36.k1.b1', '132.j1.b1'], 'core': '12.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [23533366, 22650619827, 24590313888, 23839464637, 19647222832], 'label': '4752.h.12.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.b1', 'normal_contained_in': ['4.e1.b1', '6.a1.b1', '6.d1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '36.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331617
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '12.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.c1.a1', '6.i1.a1', '6.i1.b1'], 'contains': ['24.b1.a1', '36.d1.a1', '132.e1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888, 13515287295, 23839464637], 'label': '4752.h.12.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.c1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '36.d1.a1', '132.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331618
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '12.h1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '36.e1.a1', '132.f1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 17644958238, 13640428742, 24590313888, 23839464637], 'label': '4752.h.12.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.a1', 'normal_contained_in': ['4.d1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '36.e1.a1', '132.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331619
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '132.e1.a1', 'complements': ['2376.b1.a1', '2376.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.e1.b1', '6.d1.a1', '6.i1.a1', '22.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9323045302, 22650619827, 13640428742, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.2.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.e1.b1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331620
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.h1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.f1.b1', '36.a1.a1', '132.g1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 2690543349, 10511889933, 24590313888, 23839464637], 'label': '4752.h.12.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331621
    {'ambient': '4752.h', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1320.144', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.g1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '36.j1.a1', '132.h1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888, 23839464637, 158006], 'label': '4752.h.12.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331622
    {'ambient': '4752.h', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1320.144', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.g1.b1', '6.i1.b1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.g1.b1', '36.j1.b1', '132.h1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 13640428742, 8560511, 24590313888, 23839464637], 'label': '4752.h.12.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.j1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331623
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.h1.a1'], 'contains': ['24.c1.a1', '36.d1.a1', '132.k1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 10511889933, 24590313888, 13515287295, 23839464637], 'label': '4752.h.12.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331624
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.h1.a1'], 'contains': ['24.c1.a1', '36.e1.a1', '132.l1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 17644958238, 10511889933, 24590313888, 23839464637], 'label': '4752.h.12.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331625
    {'ambient': '4752.h', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1320.144', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.g1.a1', '6.i1.b1', '6.k1.a1'], 'contains': ['24.b1.a1', '36.k1.a1', '132.m1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888, 23839464637, 57212464], 'label': '4752.h.12.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331626
    {'ambient': '4752.h', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1320.144', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.g1.b1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '36.k1.b1', '132.m1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [23533366, 16330971943, 13640428742, 24590313888, 23839464637], 'label': '4752.h.12.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.m1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331627
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '16.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '120.47', 'aut_weyl_index': 528, 'centralizer': '2.b1.a1', 'complements': ['297.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.c1.b1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 19647222832], 'label': '4752.h.16.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '528.149', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331628
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': ['264.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.h1.a1', '54.b1.a1', '198.d1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026109, 24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.18.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '36.c1.a1', '36.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331629
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': ['264.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.b1', '36.h1.b1', '54.b1.b1', '198.d1.b1'], 'core': '18.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 8560511, 19647222832, 24778026109, 23839464637], 'label': '4752.h.18.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.a1.b1', 'normal_contained_in': ['6.a1.b1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '36.c1.b1', '36.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.b1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331630
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '132.e1.a1', 'complements': ['2376.c1.a1', '2376.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.a1', '4.e1.a1', '6.d1.b1', '6.i1.b1', '22.c1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 8560511, 24590313888, 23839464637, 19647222832, 57212464], 'label': '4752.h.2.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.a1', '4.e1.a1', '6.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331631
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 792, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.h1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.d1.a1', '36.e1.a1', '54.a1.a1', '198.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 17644958238, 2690543349, 24590313888, 23839464637], 'label': '4752.h.18.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.a1'], 'normal_contains': ['36.a1.a1', '36.d1.a1', '36.e1.a1', '54.a1.a1', '198.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331632
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 792, 'centralizer': '2.b1.a1', 'complements': ['264.g1.a1', '264.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.f1.a1', '36.g1.a1', '54.a1.a1', '198.b1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026109, 24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.18.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.b1.a1', '9.a1.a1'], 'normal_contains': ['36.b1.a1', '36.f1.a1', '36.g1.a1', '54.a1.a1', '198.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331633
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': ['264.e1.a1', '264.f1.a1', '264.f1.b1', '264.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.f1.a1', '36.h1.b1', '54.c1.a1', '198.h1.a1'], 'core': '18.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 21461775264, 23839464637, 19647222832, 158006], 'label': '4752.h.18.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.a1', 'normal_contained_in': ['6.d1.a1', '9.a1.a1'], 'normal_contains': ['36.c1.a1', '36.f1.a1', '36.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331634
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '132.e1.a1', 'complements': ['264.g1.a1', '264.e1.a1', '264.f1.b1', '264.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '9.a1.a1'], 'contains': ['36.c1.b1', '36.f1.a1', '36.h1.a1', '54.c1.b1', '198.h1.b1'], 'core': '18.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [57355781, 8560511, 24590313888, 23839464637, 19647222832], 'label': '4752.h.18.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.d1.b1', 'normal_contained_in': ['6.d1.b1', '9.a1.a1'], 'normal_contains': ['36.c1.b1', '36.f1.a1', '36.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.d1.b1', 'projective_image': '1188.57', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331635
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': ['264.e1.a1', '264.f1.a1', '264.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.c1.a1', '36.c1.b1', '36.g1.a1', '54.d1.a1', '198.i1.a1'], 'core': '18.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637, 19647222832, 3378821867, 158006], 'label': '4752.h.18.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.e1.a1', 'normal_contained_in': ['6.e1.a1', '9.a1.a1'], 'normal_contains': ['36.c1.a1', '36.c1.b1', '36.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.e1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331636
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '132.e1.a1', 'complements': ['264.e1.a1', '264.f1.b1', '264.f1.a1', '264.g1.b1', '264.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.g1.a1', '36.h1.a1', '36.h1.b1', '54.e1.a1', '198.k1.a1'], 'core': '18.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [57355781, 24590313888, 23839464637, 19647222832, 3378821867], 'label': '4752.h.18.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.f1.a1', 'normal_contained_in': ['6.f1.a1', '9.a1.a1'], 'normal_contains': ['36.g1.a1', '36.h1.b1', '36.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.f1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331637
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '880.210', 'aut_weyl_index': 72, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.j1.a1', '36.k1.a1', '54.b1.a1', '198.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 2690543349, 24590313888, 23839464637, 158006], 'label': '4752.h.18.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.g1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331638
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '880.210', 'aut_weyl_index': 72, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.g1.b1', '9.b1.a1'], 'contains': ['36.a1.a1', '36.j1.b1', '36.k1.b1', '54.b1.b1', '198.c1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 2690543349, 8560511, 24590313888, 23839464637], 'label': '4752.h.18.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.g1.b1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331639
    {'ambient': '4752.h', 'aut_centralizer_order': 396, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '80.52', 'aut_weyl_index': 792, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['36.i1.a1', '36.l1.a1', '36.m1.a1', '54.a1.a1', '198.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [17644958238, 22650619827, 22713190600, 24590313888, 23839464637], 'label': '4752.h.18.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331640
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '880.210', 'aut_weyl_index': 72, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.i1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.j1.a1', '36.k1.b1', '54.c1.a1', '198.f1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 24590313888, 13515287295, 23839464637, 158006], 'label': '4752.h.18.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.i1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331641
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '132.e1.a1', 'complements': ['2376.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '6.e1.a1', '6.j1.a1', '22.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 23839464637, 19647222832, 3378821867, 158006], 'label': '4752.h.2.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.b1', '4.d1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331642
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '880.210', 'aut_weyl_index': 72, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.i1.b1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.j1.b1', '36.k1.a1', '54.c1.b1', '198.f1.b1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 8560511, 24590313888, 23839464637, 57212464], 'label': '4752.h.18.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.i1.b1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.b1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331643
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 36, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '9.b1.a1'], 'contains': ['36.e1.a1', '36.j1.a1', '36.j1.b1', '54.d1.a1', '198.g1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 17644958238, 24590313888, 23839464637, 158006], 'label': '4752.h.18.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.j1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331644
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 36, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.k1.a1', '9.b1.a1'], 'contains': ['36.e1.a1', '36.k1.a1', '36.k1.b1', '54.e1.a1', '198.j1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [16330971943, 17644958238, 24590313888, 23839464637, 57212464], 'label': '4752.h.18.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.k1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331645
    {'ambient': '4752.h', 'aut_centralizer_order': 1320, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.52', 'aut_weyl_index': 1320, 'centralizer': '2.b1.a1', 'complements': ['216.c1.a1', '216.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1', '66.a1.a1', '66.b1.a1', '66.e1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 11075027061, 19522081488, 2127406644], 'label': '4752.h.22.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1', '66.a1.a1', '66.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331647
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '144.195', 'aut_weyl_index': 440, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.d1.b1', '44.e1.b1', '66.c1.b1', '66.d1.b1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 8560511, 19522081488, 2127406644], 'label': '4752.h.22.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.b1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331648
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '144.195', 'aut_weyl_index': 440, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.d1.a1', '44.e1.b1', '66.f1.a1', '66.h1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 20898638422, 19522081488, 2127406644, 158006], 'label': '4752.h.22.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331649
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '144.195', 'aut_weyl_index': 440, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.d1.b1', '44.e1.a1', '66.f1.b1', '66.h1.b1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 57212464, 19522081488, 2127406644, 27992073], 'label': '4752.h.22.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.b1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331650
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '22.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '288.992', 'aut_weyl_index': 220, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.d1.a1', '44.d1.b1', '66.g1.a1', '66.i1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 11075027061, 19522081488, 2127406644, 158006], 'label': '4752.h.22.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.d1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331651
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '22.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '288.992', 'aut_weyl_index': 220, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.e1.a1', '44.e1.b1', '66.j1.a1', '66.k1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 11075027061, 57212464, 19522081488, 2127406644], 'label': '4752.h.22.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.e1.a1', 'projective_image': '264.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331652
    {'ambient': '4752.h', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '132.e1.a1', 'complements': ['2376.b1.a1', '2376.c1.b1', '2376.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.e1.b1', '6.f1.a1', '6.k1.a1', '22.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 13640428742, 24590313888, 23839464637, 19647222832, 57212464, 3378821867], 'label': '4752.h.2.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.b1', '4.e1.a1', '6.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331653
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '24.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.c1.b1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.f1.b1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1', '264.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 24590313888, 23839464637, 19647222832], 'label': '4752.h.24.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.c1.b1', '12.d1.a1', '12.e1.a1', '12.f1.b1', '12.f1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331654
    {'ambient': '4752.h', 'aut_centralizer_order': 1056, 'aut_label': '24.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.g1.a1', '12.h1.a1', '12.j1.a1', '12.j1.b1', '12.m1.a1', '12.m1.b1'], 'contains': ['48.b1.a1', '72.a1.a1', '264.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888, 23839464637], 'label': '4752.h.24.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1', '12.g1.a1', '12.h1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1', '264.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '264.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331655
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.i1.a1', '12.k1.a1', '12.l1.a1'], 'contains': ['48.c1.a1', '72.a1.a1', '264.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 10511889933, 24590313888, 23839464637], 'label': '4752.h.24.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '792.134', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331656
    {'ambient': '4752.h', 'aut_centralizer_order': 792, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.f1.b1', '264.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888, 19647222832], 'label': '4752.h.24.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331657
    {'ambient': '4752.h', 'aut_centralizer_order': 528, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.d1.a1', '264.e1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 2690543349, 13640428742, 24590313888], 'label': '4752.h.24.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331658
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.i1.a1'], 'contains': ['48.c1.a1', '72.d1.a1', '264.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 2690543349, 21774629051, 24590313888], 'label': '4752.h.24.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331659
    {'ambient': '4752.h', 'aut_centralizer_order': 264, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '60.13', 'aut_weyl_index': 1056, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.i1.a1'], 'contains': ['48.c1.a1', '72.d1.a1', '264.f1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [16330971943, 2690543349, 10511889933, 24590313888], 'label': '4752.h.24.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.f1.b1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 60331660
    {'ambient': '4752.h', 'aut_centralizer_order': 8, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.17', 'aut_weyl_index': 96, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.j1.a1'], 'contains': ['48.b1.a1', '72.g1.a1', '264.g1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16330971943, 13640428742, 24590313888, 158006], 'label': '4752.h.24.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '24.g1.a1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60331661
    {'ambient': '4752.h', 'aut_centralizer_order': 8, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '660.17', 'aut_weyl_index': 96, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.j1.b1'], 'contains': ['48.b1.a1', '72.g1.b1', '264.g1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [16330971943, 13640428742, 8560511, 24590313888], 'label': '4752.h.24.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '24.g1.b1', 'projective_image': '528.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 60331662
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '72.g1.a1', '72.h1.a1', '264.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 24590313888, 19647222832, 158006], 'label': '4752.h.24.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.h1.a1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '66.3'}
  • id: 60331663
    {'ambient': '4752.h', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 3, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.b1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.f1.a1', '9.a1.a1', '9.b1.a1', '33.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [22650619827, 22713190600, 24590313888, 23839464637, 19647222832, 3378821867, 158006], 'label': '4752.h.3.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.a1.b1', '6.b1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.f1.a1', '9.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331664
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.c1.b1'], 'contains': ['48.a1.a1', '72.g1.b1', '72.h1.b1', '264.h1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [22650619827, 8560511, 24590313888, 19647222832], 'label': '4752.h.24.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '24.h1.b1', 'projective_image': '1584.621', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': '66.3'}
  • id: 60331665
    {'ambient': '4752.h', 'aut_centralizer_order': 12, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 36, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.b1.b1', '54.c1.a1', '54.c1.b1', '54.d1.a1', '54.e1.a1', '297.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [17644958238, 24778026109, 24590313888, 23839464637, 158006], 'label': '4752.h.27.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '27.a1.a1', 'projective_image': '1188.57', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
  • id: 60331666
    {'ambient': '4752.h', 'aut_centralizer_order': 20, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 33, 'aut_weyl_group': '96.221', 'aut_weyl_index': 660, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '11.a1.a1'], 'contains': ['66.b1.a1', '66.c1.a1', '66.c1.b1', '66.f1.a1', '66.f1.b1', '66.g1.a1', '66.k1.a1', '99.a1.a1'], 'core': '66.b1.a1', 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [24778026504, 2127406316, 3941959033, 2189977417, 19522081488, 158006], 'label': '4752.h.33.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '33.a1.a1', 'old_label': '33.a1.a1', 'projective_image': '132.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 60331667
    {'ambient': '4752.h', 'aut_centralizer_order': 30, 'aut_label': '33.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 330, 'centralizer': '132.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a1'], 'contains': ['66.a1.a1', '66.d1.a1', '66.d1.b1', '66.h1.a1', '66.h1.b1', '66.i1.a1', '66.j1.a1', '99.a1.a1', '99.b1.a1'], 'core': '66.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': None, 'generators': [24778026504, 22650619827, 22713190600, 11075027061, 2127406644, 158006], 'label': '4752.h.33.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '33.b1.a1', 'projective_image': '396.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 60331668
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.i1.a1', '18.b1.a1', '18.g1.a1', '18.g1.b1'], 'contains': ['72.a1.a1', '72.d1.a1', '108.a1.a1', '396.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 2690543349, 24590313888, 23839464637], 'label': '4752.h.36.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1', '18.b1.a1'], 'normal_contains': ['72.a1.a1', '108.a1.a1', '396.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331669
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '36.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1', '18.a1.b1', '18.c1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '108.a1.a1', '396.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24778026109, 24590313888, 23839464637, 19647222832], 'label': '4752.h.36.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '18.a1.a1', '18.a1.b1', '18.c1.a1'], 'normal_contains': ['72.b1.a1', '108.a1.a1', '396.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331670
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1', '18.d1.a1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.h1.a1', '108.d1.a1', '396.i1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [24590313888, 23839464637, 19647222832, 158006], 'label': '4752.h.36.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.c1.a1', '18.a1.a1', '18.d1.a1', '18.e1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331671
    {'ambient': '4752.h', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1320.142', 'aut_weyl_index': 48, 'centralizer': '132.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '18.a1.b1', '18.d1.b1', '18.e1.a1'], 'contains': ['72.b1.a1', '72.h1.b1', '108.d1.b1', '396.i1.b1'], 'core': '36.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [8560511, 24590313888, 23839464637, 19647222832], 'label': '4752.h.36.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.c1.b1', 'normal_contained_in': ['12.c1.b1', '18.a1.b1', '18.d1.b1', '18.e1.a1'], 'normal_contains': ['72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '132.9'}
  • id: 60331672
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '36.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.a1', '12.k1.a1', '18.b1.a1', '18.i1.a1', '18.i1.b1'], 'contains': ['72.a1.a1', '108.b1.a1', '396.c1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 24590313888, 13515287295, 23839464637], 'label': '4752.h.36.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.d1.a1', 'normal_contained_in': ['12.d1.a1', '12.g1.a1', '18.b1.a1'], 'normal_contains': ['72.a1.a1', '108.b1.a1', '396.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '396.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 60331673
    {'ambient': '4752.h', 'aut_centralizer_order': 1584, 'aut_label': '36.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 1584, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.h1.a1', '12.l1.a1', '18.b1.a1', '18.j1.a1', '18.k1.a1'], 'contains': ['72.a1.a1', '108.c1.a1', '396.d1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [16330971943, 17644958238, 24590313888, 23839464637], 'label': '4752.h.36.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.e1.a1', 'normal_contained_in': ['12.e1.a1', '12.h1.a1', '18.b1.a1'], 'normal_contains': ['72.a1.a1', '108.c1.a1', '396.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '792.134', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}