Abstract group data - 960.10116

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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': '160.228', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 4, 4, 4, 4, 2, 12, 12, 12], 'aut_gens': [[1, 2, 4, 16], [481, 10, 644, 664], [481, 482, 484, 112], [1, 2, 12, 120], [482, 489, 172, 280], [9, 490, 164, 760], [490, 9, 332, 464], [9, 490, 4, 952], [481, 2, 172, 120], [10, 489, 812, 16], [9, 482, 172, 592]], 'aut_group': None, 'aut_hash': 1392258107361899436, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 28, 'aut_perms': [225219168818687021866319218376, 250863447509107528385551973880, 192244862969354136061116092488, 228349004818947634525044114643, 194837614516948419309561481038, 10504214637516591272919249558, 195044907320009045727130792620, 193421239897642450578334593461, 1358098340504805281729478449, 8415737958413168899651886025], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 4, 1], [2, 6, 2, 1], [3, 2, 1, 1], [4, 1, 4, 1], [4, 2, 2, 2], [4, 2, 4, 1], [4, 3, 4, 2], [4, 6, 2, 1], [4, 6, 4, 2], [5, 1, 4, 1], [6, 2, 1, 3], [6, 4, 4, 1], [10, 1, 4, 3], [10, 2, 16, 1], [10, 6, 8, 1], [12, 2, 4, 1], [12, 4, 2, 2], [12, 4, 4, 1], [15, 2, 4, 1], [20, 1, 16, 1], [20, 2, 8, 2], [20, 2, 16, 1], [20, 3, 16, 2], [20, 6, 8, 1], [20, 6, 16, 2], [30, 2, 4, 3], [30, 4, 16, 1], [60, 2, 16, 1], [60, 4, 8, 2], [60, 4, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4\\times C_4\\times C_2^2\\wr C_2\\times S_3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 1718285292446712972, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [2, 6, 2], [3, 2, 1], [4, 1, 4], [4, 2, 8], [4, 3, 8], [4, 6, 10], [5, 1, 4], [6, 2, 3], [6, 4, 4], [10, 1, 12], [10, 2, 16], [10, 6, 8], [12, 2, 4], [12, 4, 8], [15, 2, 4], [20, 1, 16], [20, 2, 32], [20, 3, 32], [20, 6, 40], [30, 2, 12], [30, 4, 16], [60, 2, 16], [60, 4, 32]], 'center_label': '40.9', 'center_order': 40, 'central_product': True, 'central_quotient': '24.14', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10116, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['48.39', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [2, 6, 1, 2], [3, 2, 1, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 3], [4, 3, 2, 4], [4, 6, 1, 4], [4, 6, 2, 3], [5, 1, 4, 1], [6, 2, 1, 3], [6, 4, 1, 4], [10, 1, 4, 3], [10, 2, 4, 4], [10, 6, 4, 2], [12, 2, 2, 2], [12, 4, 1, 2], [12, 4, 2, 3], [15, 2, 4, 1], [20, 1, 8, 2], [20, 2, 4, 2], [20, 2, 8, 3], [20, 3, 8, 4], [20, 6, 4, 4], [20, 6, 8, 3], [30, 2, 4, 3], [30, 4, 4, 4], [60, 2, 8, 2], [60, 4, 4, 2], [60, 4, 8, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 20442240, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '240.206', 'hash': 10116, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 2, 3], 'inner_gens': [[1, 490, 4, 16], [489, 2, 4, 16], [1, 2, 4, 656], [1, 2, 324, 16]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_2\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 160], [2, 120], [4, 20]], 'label': '960.10116', 'linC_count': 1536, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 256, 'linQ_dim': 12, 'linQ_dim_count': 4352, 'linR_count': 6528, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D4:S3*C20', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 48, 'number_characteristic_subgroups': 86, 'number_conjugacy_classes': 300, 'number_divisions': 86, 'number_normal_subgroups': 314, 'number_subgroup_autclasses': 312, 'number_subgroup_classes': 620, 'number_subgroups': 1232, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 23], [3, 2], [4, 104], [5, 4], [6, 22], [10, 92], [12, 40], [15, 8], [20, 416], [30, 88], [60, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 2, 4, 4], 'outer_gen_pows': [320, 0, 0, 320, 640, 0, 0], 'outer_gens': [[490, 481, 172, 696], [9, 482, 12, 272], [1, 10, 812, 760], [1, 482, 644, 688], [9, 482, 652, 792], [2, 481, 4, 664], [490, 481, 172, 952]], 'outer_group': '512.10493066', 'outer_hash': 4599981025227913554, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 256, 'outer_perms': [194644722186931462180186344807959092113198783733230570106026076503726368809655016774550066428604440678982984426647119164265124184397271329883803644422770588779900423995241128599567685078823668159566281951690230048499537207362017867959945380246921637612345777734426808737652209175592884655904727030125750750091258925348477982391089578188084030138144112226131128031309093235372773905513771104242996306002416340787520432423414869953761164022882263571456499672791826869925265498835016273356116794244401702214593, 760414654939635102964368659057670575102761508655884957307818172781364909419529796522421845874585288810113830729920751010632714360904654574702998878527304959171784141610962596847590773359564183439152963795861372897988076613700244529301433441681984803328098227453552684590723365836284922293434551053942659173570553412779738202473597814062540880014920994408306355791544730960637894082561297550619171500929063130261826147854631163857858854916267302240880605976383975966823235973126995613216713981058244571685591, 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70937637563208330617951892200931777963406393030553343277334848158408233549068966256456497265317462469318797818283902594538419623425579663318610767484288844672877227060792120684910577748138289519486804221812372207690769475471338039733114568645095704218010989770742889918712891393374829588072016433598988482325274535128424607974020062432453033648597068922881577429142018625792290692117665135214966925777828540773140174359305261844736910104382906094971814127246644776899679376590938210982315211664507832081642, 383391541482320737503477515932221670755545111991424341784354404565634426461859255482505268913935289549776121373439279563616825926295292420552939587237079334133282516743981202331820508223611950767880596222155590457772782531827141447176733614979841703596096382390147268770631796795518432276434305998158071176557593141613637198444773197917330459141233853739770082698262096296368676461613979253414118288336630827182957806856678697902858535111945180259872350714665643979741233375848996940950968156212858494477989, 592463585437418437917101321843734088215665065387529524051707426140276533295854305835683508174806183070150651267451071222497699392799315673761041152388861642037814433407073572587562750416008024551033009140797752563564984100392827156760767340739140502609015271205924809017770741654243548281435402057225867412844392905609458049328975887038917729170807311431917681256283304440582524454520149574550746243774043444682632180640526238994396805953534306536460218503942008805274981176083612642838098040027462466745070], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2.C_2^5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 26], [8, 17], [16, 10], [32, 1]], 'representations': {'PC': {'code': 13556277927161114599785779628185223175, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 7841, 66, 6580, 116, 4245, 141, 9878, 222]}, 'GLZN': {'d': 2, 'p': 110, 'gens': [1331089, 89183117, 118459089, 107811081, 1461921, 145079109, 75207551, 60170925]}, 'Perm': {'d': 20, 'gens': [128800787959468809, 64250400614400, 262560264661094409, 391971468784896016, 46200, 16, 262560264661094416, 43545600]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4:S_3\\times C_{20}', 'transitive_degree': 480, '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: 142439343
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 10116, 'group_order': 960, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 142439454
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 10116, 'group_order': 960, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8, 'size': 1}
  • id: 142439565
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 10116, 'group_order': 960, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 488, 'size': 1}
  • id: 142439577
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 10116, 'group_order': 960, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 480, 'size': 1}
  • id: 142439588
    {'aut_label': '2D', 'centralizer': '2.c1.a1', 'counter': 5, 'group_counter': 10116, 'group_order': 960, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 2, 'size': 2}
  • id: 142439599
    {'aut_label': '2D', 'centralizer': '2.c1.a1', 'counter': 6, 'group_counter': 10116, 'group_order': 960, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 482, 'size': 2}
  • id: 142439610
    {'aut_label': '2D', 'centralizer': '2.c1.b1', 'counter': 7, 'group_counter': 10116, 'group_order': 960, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 1, 'size': 2}
  • id: 142439621
    {'aut_label': '2D', 'centralizer': '2.c1.b1', 'counter': 8, 'group_counter': 10116, 'group_order': 960, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 481, 'size': 2}
  • id: 142439632
    {'aut_label': '2H', 'centralizer': '6.h1.a1', 'counter': 9, 'group_counter': 10116, 'group_order': 960, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 407, 'size': 6}
  • id: 142439344
    {'aut_label': '2H', 'centralizer': '6.h1.a1', 'counter': 10, 'group_counter': 10116, 'group_order': 960, 'label': '2I', 'order': 2, 'powers': [1, 10, 10], 'representative': 247, 'size': 6}
  • id: 142439355
    {'aut_label': '3A', 'centralizer': '2.f1.a1', 'counter': 11, 'group_counter': 10116, 'group_order': 960, 'label': '3A', 'order': 3, 'powers': [11, 1, 11], 'representative': 640, 'size': 2}
  • id: 142439366
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 10116, 'group_order': 960, 'label': '4A1', 'order': 4, 'powers': [4, 13, 12], 'representative': 240, 'size': 1}
  • id: 142439377
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 10116, 'group_order': 960, 'label': '4A-1', 'order': 4, 'powers': [4, 12, 13], 'representative': 720, 'size': 1}
  • id: 142439388
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 10116, 'group_order': 960, 'label': '4B1', 'order': 4, 'powers': [4, 15, 14], 'representative': 248, 'size': 1}
  • id: 142439399
    {'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 10116, 'group_order': 960, 'label': '4B-1', 'order': 4, 'powers': [4, 14, 15], 'representative': 728, 'size': 1}
  • id: 142439410
    {'aut_label': '4C', 'centralizer': '2.h1.a1', 'counter': 16, 'group_counter': 10116, 'group_order': 960, 'label': '4C', 'order': 4, 'powers': [3, 16, 16], 'representative': 491, 'size': 2}
  • id: 142439421
    {'aut_label': '4C', 'centralizer': '2.h1.a1', 'counter': 17, 'group_counter': 10116, 'group_order': 960, 'label': '4D', 'order': 4, 'powers': [3, 17, 17], 'representative': 11, 'size': 2}
  • id: 142439432
    {'aut_label': '4E1', 'centralizer': '2.c1.a1', 'counter': 18, 'group_counter': 10116, 'group_order': 960, 'label': '4E1', 'order': 4, 'powers': [4, 19, 18], 'representative': 242, 'size': 2}
  • id: 142439443
    {'aut_label': '4E1', 'centralizer': '2.c1.a1', 'counter': 19, 'group_counter': 10116, 'group_order': 960, 'label': '4E-1', 'order': 4, 'powers': [4, 18, 19], 'representative': 722, 'size': 2}
  • id: 142439455
    {'aut_label': '4E1', 'centralizer': '2.c1.b1', 'counter': 20, 'group_counter': 10116, 'group_order': 960, 'label': '4F1', 'order': 4, 'powers': [4, 21, 20], 'representative': 241, 'size': 2}
  • id: 142439466
    {'aut_label': '4E1', 'centralizer': '2.c1.b1', 'counter': 21, 'group_counter': 10116, 'group_order': 960, 'label': '4F-1', 'order': 4, 'powers': [4, 20, 21], 'representative': 721, 'size': 2}
  • id: 142439477
    {'aut_label': '4G1', 'centralizer': '2.h1.a1', 'counter': 22, 'group_counter': 10116, 'group_order': 960, 'label': '4G1', 'order': 4, 'powers': [2, 23, 22], 'representative': 731, 'size': 2}
  • id: 142439488
    {'aut_label': '4G1', 'centralizer': '2.h1.a1', 'counter': 23, 'group_counter': 10116, 'group_order': 960, 'label': '4G-1', 'order': 4, 'powers': [2, 22, 23], 'representative': 723, 'size': 2}
  • id: 142439499
    {'aut_label': '4H1', 'centralizer': '3.a1.a1', 'counter': 24, 'group_counter': 10116, 'group_order': 960, 'label': '4H1', 'order': 4, 'powers': [2, 25, 24], 'representative': 4, 'size': 3}
  • id: 142439510
    {'aut_label': '4H1', 'centralizer': '3.a1.a1', 'counter': 25, 'group_counter': 10116, 'group_order': 960, 'label': '4H-1', 'order': 4, 'powers': [2, 24, 25], 'representative': 12, 'size': 3}
  • id: 142439521
    {'aut_label': '4H1', 'centralizer': '3.a1.a1', 'counter': 26, 'group_counter': 10116, 'group_order': 960, 'label': '4I1', 'order': 4, 'powers': [2, 27, 26], 'representative': 804, 'size': 3}
  • id: 142439532
    {'aut_label': '4H1', 'centralizer': '3.a1.a1', 'counter': 27, 'group_counter': 10116, 'group_order': 960, 'label': '4I-1', 'order': 4, 'powers': [2, 26, 27], 'representative': 812, 'size': 3}
  • id: 142439543
    {'aut_label': '4J1', 'centralizer': '3.a1.a1', 'counter': 28, 'group_counter': 10116, 'group_order': 960, 'label': '4J1', 'order': 4, 'powers': [3, 29, 28], 'representative': 404, 'size': 3}
  • id: 142439554
    {'aut_label': '4J1', 'centralizer': '3.a1.a1', 'counter': 29, 'group_counter': 10116, 'group_order': 960, 'label': '4J-1', 'order': 4, 'powers': [3, 28, 29], 'representative': 892, 'size': 3}
  • id: 142439566
    {'aut_label': '4J1', 'centralizer': '3.a1.a1', 'counter': 30, 'group_counter': 10116, 'group_order': 960, 'label': '4K1', 'order': 4, 'powers': [3, 31, 30], 'representative': 244, 'size': 3}
  • id: 142439568
    {'aut_label': '4J1', 'centralizer': '3.a1.a1', 'counter': 31, 'group_counter': 10116, 'group_order': 960, 'label': '4K-1', 'order': 4, 'powers': [3, 30, 31], 'representative': 732, 'size': 3}
  • id: 142439569
    {'aut_label': '4L', 'centralizer': '6.d1.a1', 'counter': 32, 'group_counter': 10116, 'group_order': 960, 'label': '4L', 'order': 4, 'powers': [3, 32, 32], 'representative': 406, 'size': 6}
  • id: 142439570
    {'aut_label': '4L', 'centralizer': '6.d1.b1', 'counter': 33, 'group_counter': 10116, 'group_order': 960, 'label': '4M', 'order': 4, 'powers': [3, 33, 33], 'representative': 405, 'size': 6}
  • id: 142439571
    {'aut_label': '4L', 'centralizer': '6.d1.a1', 'counter': 34, 'group_counter': 10116, 'group_order': 960, 'label': '4N', 'order': 4, 'powers': [3, 34, 34], 'representative': 246, 'size': 6}
  • id: 142439572
    {'aut_label': '4L', 'centralizer': '6.d1.b1', 'counter': 35, 'group_counter': 10116, 'group_order': 960, 'label': '4O', 'order': 4, 'powers': [3, 35, 35], 'representative': 245, 'size': 6}
  • id: 142439573
    {'aut_label': '4P1', 'centralizer': '6.d1.a1', 'counter': 36, 'group_counter': 10116, 'group_order': 960, 'label': '4P1', 'order': 4, 'powers': [2, 37, 36], 'representative': 6, 'size': 6}
  • id: 142439574
    {'aut_label': '4P1', 'centralizer': '6.d1.a1', 'counter': 37, 'group_counter': 10116, 'group_order': 960, 'label': '4P-1', 'order': 4, 'powers': [2, 36, 37], 'representative': 14, 'size': 6}
  • id: 142439575
    {'aut_label': '4P1', 'centralizer': '6.d1.b1', 'counter': 38, 'group_counter': 10116, 'group_order': 960, 'label': '4Q1', 'order': 4, 'powers': [2, 39, 38], 'representative': 5, 'size': 6}
  • id: 142439576
    {'aut_label': '4P1', 'centralizer': '6.d1.b1', 'counter': 39, 'group_counter': 10116, 'group_order': 960, 'label': '4Q-1', 'order': 4, 'powers': [2, 38, 39], 'representative': 13, 'size': 6}
  • id: 142439578
    {'aut_label': '4R1', 'centralizer': '6.h1.a1', 'counter': 40, 'group_counter': 10116, 'group_order': 960, 'label': '4R1', 'order': 4, 'powers': [4, 41, 40], 'representative': 7, 'size': 6}
  • id: 142439579
    {'aut_label': '4R1', 'centralizer': '6.h1.a1', 'counter': 41, 'group_counter': 10116, 'group_order': 960, 'label': '4R-1', 'order': 4, 'powers': [4, 40, 41], 'representative': 487, 'size': 6}
  • id: 142439580
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 42, 'group_counter': 10116, 'group_order': 960, 'label': '5A1', 'order': 5, 'powers': [44, 45, 1], 'representative': 192, 'size': 1}
  • id: 142439581
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 43, 'group_counter': 10116, 'group_order': 960, 'label': '5A-1', 'order': 5, 'powers': [45, 44, 1], 'representative': 768, 'size': 1}
  • id: 142439582
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 44, 'group_counter': 10116, 'group_order': 960, 'label': '5A2', 'order': 5, 'powers': [43, 42, 1], 'representative': 384, 'size': 1}
  • id: 142439583
    {'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 45, 'group_counter': 10116, 'group_order': 960, 'label': '5A-2', 'order': 5, 'powers': [42, 43, 1], 'representative': 576, 'size': 1}
  • id: 142439584
    {'aut_label': '6A', 'centralizer': '2.f1.a1', 'counter': 46, 'group_counter': 10116, 'group_order': 960, 'label': '6A', 'order': 6, 'powers': [11, 4, 46], 'representative': 160, 'size': 2}
  • id: 142439585
    {'aut_label': '6B', 'centralizer': '2.f1.a1', 'counter': 47, 'group_counter': 10116, 'group_order': 960, 'label': '6B', 'order': 6, 'powers': [11, 3, 47], 'representative': 168, 'size': 2}
  • id: 142439586
    {'aut_label': '6C', 'centralizer': '2.f1.a1', 'counter': 48, 'group_counter': 10116, 'group_order': 960, 'label': '6C', 'order': 6, 'powers': [11, 2, 48], 'representative': 648, 'size': 2}
  • id: 142439587
    {'aut_label': '6D', 'centralizer': '4.b1.a1', 'counter': 49, 'group_counter': 10116, 'group_order': 960, 'label': '6D', 'order': 6, 'powers': [11, 5, 49], 'representative': 322, 'size': 4}
  • id: 142439589
    {'aut_label': '6D', 'centralizer': '4.b1.a1', 'counter': 50, 'group_counter': 10116, 'group_order': 960, 'label': '6E', 'order': 6, 'powers': [11, 6, 50], 'representative': 162, 'size': 4}
  • id: 142439590
    {'aut_label': '6D', 'centralizer': '4.b1.b1', 'counter': 51, 'group_counter': 10116, 'group_order': 960, 'label': '6F', 'order': 6, 'powers': [11, 7, 51], 'representative': 321, 'size': 4}
  • id: 142439591
    {'aut_label': '6D', 'centralizer': '4.b1.b1', 'counter': 52, 'group_counter': 10116, 'group_order': 960, 'label': '6G', 'order': 6, 'powers': [11, 8, 52], 'representative': 161, 'size': 4}
  • id: 142439592
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 53, 'group_counter': 10116, 'group_order': 960, 'label': '10A1', 'order': 10, 'powers': [43, 55, 2], 'representative': 392, 'size': 1}
  • id: 142439593
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 54, 'group_counter': 10116, 'group_order': 960, 'label': '10A-1', 'order': 10, 'powers': [42, 56, 2], 'representative': 584, 'size': 1}
  • id: 142439594
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 55, 'group_counter': 10116, 'group_order': 960, 'label': '10A3', 'order': 10, 'powers': [44, 54, 2], 'representative': 200, 'size': 1}
  • id: 142439595
    {'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 56, 'group_counter': 10116, 'group_order': 960, 'label': '10A-3', 'order': 10, 'powers': [45, 53, 2], 'representative': 776, 'size': 1}
  • id: 142439596
    {'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 57, 'group_counter': 10116, 'group_order': 960, 'label': '10B1', 'order': 10, 'powers': [44, 59, 3], 'representative': 680, 'size': 1}
  • id: 142439597
    {'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 58, 'group_counter': 10116, 'group_order': 960, 'label': '10B-1', 'order': 10, 'powers': [45, 60, 3], 'representative': 296, 'size': 1}
  • id: 142439598
    {'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 59, 'group_counter': 10116, 'group_order': 960, 'label': '10B3', 'order': 10, 'powers': [42, 58, 3], 'representative': 104, 'size': 1}
  • id: 142439600
    {'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 60, 'group_counter': 10116, 'group_order': 960, 'label': '10B-3', 'order': 10, 'powers': [43, 57, 3], 'representative': 872, 'size': 1}
  • id: 142439601
    {'aut_label': '10C1', 'centralizer': '1.a1.a1', 'counter': 61, 'group_counter': 10116, 'group_order': 960, 'label': '10C1', 'order': 10, 'powers': [43, 63, 4], 'representative': 864, 'size': 1}
  • id: 142439602
    {'aut_label': '10C1', 'centralizer': '1.a1.a1', 'counter': 62, 'group_counter': 10116, 'group_order': 960, 'label': '10C-1', 'order': 10, 'powers': [42, 64, 4], 'representative': 96, 'size': 1}
  • id: 142439603
    {'aut_label': '10C1', 'centralizer': '1.a1.a1', 'counter': 63, 'group_counter': 10116, 'group_order': 960, 'label': '10C3', 'order': 10, 'powers': [44, 62, 4], 'representative': 672, 'size': 1}
  • id: 142439604
    {'aut_label': '10C1', 'centralizer': '1.a1.a1', 'counter': 64, 'group_counter': 10116, 'group_order': 960, 'label': '10C-3', 'order': 10, 'powers': [45, 61, 4], 'representative': 288, 'size': 1}
  • id: 142439605
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 65, 'group_counter': 10116, 'group_order': 960, 'label': '10D1', 'order': 10, 'powers': [44, 67, 5], 'representative': 194, 'size': 2}
  • id: 142439606
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 66, 'group_counter': 10116, 'group_order': 960, 'label': '10D-1', 'order': 10, 'powers': [45, 68, 5], 'representative': 770, 'size': 2}
  • id: 142439607
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 67, 'group_counter': 10116, 'group_order': 960, 'label': '10D3', 'order': 10, 'powers': [42, 66, 5], 'representative': 578, 'size': 2}
  • id: 142439608
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 68, 'group_counter': 10116, 'group_order': 960, 'label': '10D-3', 'order': 10, 'powers': [43, 65, 5], 'representative': 386, 'size': 2}
  • id: 142439609
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 69, 'group_counter': 10116, 'group_order': 960, 'label': '10E1', 'order': 10, 'powers': [42, 71, 6], 'representative': 98, 'size': 2}
  • id: 142439611
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 70, 'group_counter': 10116, 'group_order': 960, 'label': '10E-1', 'order': 10, 'powers': [43, 72, 6], 'representative': 866, 'size': 2}
  • id: 142439612
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 71, 'group_counter': 10116, 'group_order': 960, 'label': '10E3', 'order': 10, 'powers': [45, 70, 6], 'representative': 290, 'size': 2}
  • id: 142439613
    {'aut_label': '10D1', 'centralizer': '2.c1.a1', 'counter': 72, 'group_counter': 10116, 'group_order': 960, 'label': '10E-3', 'order': 10, 'powers': [44, 69, 6], 'representative': 674, 'size': 2}
  • id: 142439614
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 73, 'group_counter': 10116, 'group_order': 960, 'label': '10F1', 'order': 10, 'powers': [44, 75, 7], 'representative': 193, 'size': 2}
  • id: 142439615
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 74, 'group_counter': 10116, 'group_order': 960, 'label': '10F-1', 'order': 10, 'powers': [45, 76, 7], 'representative': 769, 'size': 2}
  • id: 142439616
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 75, 'group_counter': 10116, 'group_order': 960, 'label': '10F3', 'order': 10, 'powers': [42, 74, 7], 'representative': 577, 'size': 2}
  • id: 142439617
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 76, 'group_counter': 10116, 'group_order': 960, 'label': '10F-3', 'order': 10, 'powers': [43, 73, 7], 'representative': 385, 'size': 2}
  • id: 142439618
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 77, 'group_counter': 10116, 'group_order': 960, 'label': '10G1', 'order': 10, 'powers': [42, 79, 8], 'representative': 97, 'size': 2}
  • id: 142439619
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 78, 'group_counter': 10116, 'group_order': 960, 'label': '10G-1', 'order': 10, 'powers': [43, 80, 8], 'representative': 865, 'size': 2}
  • id: 142439620
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 79, 'group_counter': 10116, 'group_order': 960, 'label': '10G3', 'order': 10, 'powers': [45, 78, 8], 'representative': 289, 'size': 2}
  • id: 142439622
    {'aut_label': '10D1', 'centralizer': '2.c1.b1', 'counter': 80, 'group_counter': 10116, 'group_order': 960, 'label': '10G-3', 'order': 10, 'powers': [44, 77, 8], 'representative': 673, 'size': 2}
  • id: 142439623
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 81, 'group_counter': 10116, 'group_order': 960, 'label': '10H1', 'order': 10, 'powers': [42, 83, 9], 'representative': 23, 'size': 6}
  • id: 142439624
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 82, 'group_counter': 10116, 'group_order': 960, 'label': '10H-1', 'order': 10, 'powers': [43, 84, 9], 'representative': 151, 'size': 6}
  • id: 142439625
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 83, 'group_counter': 10116, 'group_order': 960, 'label': '10H3', 'order': 10, 'powers': [45, 82, 9], 'representative': 215, 'size': 6}
  • id: 142439626
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 84, 'group_counter': 10116, 'group_order': 960, 'label': '10H-3', 'order': 10, 'powers': [44, 81, 9], 'representative': 599, 'size': 6}
  • id: 142439627
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 85, 'group_counter': 10116, 'group_order': 960, 'label': '10I1', 'order': 10, 'powers': [45, 87, 10], 'representative': 55, 'size': 6}
  • id: 142439628
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 86, 'group_counter': 10116, 'group_order': 960, 'label': '10I-1', 'order': 10, 'powers': [44, 88, 10], 'representative': 119, 'size': 6}
  • id: 142439629
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 87, 'group_counter': 10116, 'group_order': 960, 'label': '10I3', 'order': 10, 'powers': [43, 86, 10], 'representative': 159, 'size': 6}
  • id: 142439630
    {'aut_label': '10H1', 'centralizer': '6.h1.a1', 'counter': 88, 'group_counter': 10116, 'group_order': 960, 'label': '10I-3', 'order': 10, 'powers': [42, 85, 10], 'representative': 31, 'size': 6}
  • id: 142439631
    {'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 89, 'group_counter': 10116, 'group_order': 960, 'label': '12A1', 'order': 12, 'powers': [46, 12, 89], 'representative': 80, 'size': 2}
  • id: 142439633
    {'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 90, 'group_counter': 10116, 'group_order': 960, 'label': '12A-1', 'order': 12, 'powers': [46, 13, 90], 'representative': 880, 'size': 2}
  • id: 142439634
    {'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 91, 'group_counter': 10116, 'group_order': 960, 'label': '12B1', 'order': 12, 'powers': [46, 14, 91], 'representative': 88, 'size': 2}
  • id: 142439635
    {'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 92, 'group_counter': 10116, 'group_order': 960, 'label': '12B-1', 'order': 12, 'powers': [46, 15, 92], 'representative': 888, 'size': 2}
  • id: 142439636
    {'aut_label': '12C', 'centralizer': '4.l1.a1', 'counter': 93, 'group_counter': 10116, 'group_order': 960, 'label': '12C', 'order': 12, 'powers': [47, 16, 93], 'representative': 323, 'size': 4}
  • id: 142439637
    {'aut_label': '12C', 'centralizer': '4.l1.a1', 'counter': 94, 'group_counter': 10116, 'group_order': 960, 'label': '12D', 'order': 12, 'powers': [47, 17, 94], 'representative': 163, 'size': 4}
  • id: 142439638
    {'aut_label': '12E1', 'centralizer': '4.b1.a1', 'counter': 95, 'group_counter': 10116, 'group_order': 960, 'label': '12E1', 'order': 12, 'powers': [46, 18, 95], 'representative': 82, 'size': 4}
  • id: 142439639
    {'aut_label': '12E1', 'centralizer': '4.b1.a1', 'counter': 96, 'group_counter': 10116, 'group_order': 960, 'label': '12E-1', 'order': 12, 'powers': [46, 19, 96], 'representative': 882, 'size': 4}
  • id: 142439640
    {'aut_label': '12E1', 'centralizer': '4.b1.b1', 'counter': 97, 'group_counter': 10116, 'group_order': 960, 'label': '12F1', 'order': 12, 'powers': [46, 20, 97], 'representative': 81, 'size': 4}
  • id: 142439641
    {'aut_label': '12E1', 'centralizer': '4.b1.b1', 'counter': 98, 'group_counter': 10116, 'group_order': 960, 'label': '12F-1', 'order': 12, 'powers': [46, 21, 98], 'representative': 881, 'size': 4}
  • id: 142439642
    {'aut_label': '12G1', 'centralizer': '4.l1.a1', 'counter': 99, 'group_counter': 10116, 'group_order': 960, 'label': '12G1', 'order': 12, 'powers': [48, 22, 99], 'representative': 83, 'size': 4}
  • id: 142439345
    {'aut_label': '12G1', 'centralizer': '4.l1.a1', 'counter': 100, 'group_counter': 10116, 'group_order': 960, 'label': '12G-1', 'order': 12, 'powers': [48, 23, 100], 'representative': 411, 'size': 4}
  • id: 142439346
    {'aut_label': '15A1', 'centralizer': '2.f1.a1', 'counter': 101, 'group_counter': 10116, 'group_order': 960, 'label': '15A1', 'order': 15, 'powers': [103, 44, 11], 'representative': 128, 'size': 2}
  • id: 142439347
    {'aut_label': '15A1', 'centralizer': '2.f1.a1', 'counter': 102, 'group_counter': 10116, 'group_order': 960, 'label': '15A-1', 'order': 15, 'powers': [104, 45, 11], 'representative': 832, 'size': 2}
  • id: 142439348
    {'aut_label': '15A1', 'centralizer': '2.f1.a1', 'counter': 103, 'group_counter': 10116, 'group_order': 960, 'label': '15A2', 'order': 15, 'powers': [102, 43, 11], 'representative': 256, 'size': 2}
  • id: 142439349
    {'aut_label': '15A1', 'centralizer': '2.f1.a1', 'counter': 104, 'group_counter': 10116, 'group_order': 960, 'label': '15A-2', 'order': 15, 'powers': [101, 42, 11], 'representative': 704, 'size': 2}
  • id: 142439350
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 105, 'group_counter': 10116, 'group_order': 960, 'label': '20A1', 'order': 20, 'powers': [62, 107, 12], 'representative': 48, 'size': 1}
  • id: 142439351
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 106, 'group_counter': 10116, 'group_order': 960, 'label': '20A-1', 'order': 20, 'powers': [61, 108, 13], 'representative': 912, 'size': 1}
  • id: 142439352
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 107, 'group_counter': 10116, 'group_order': 960, 'label': '20A3', 'order': 20, 'powers': [64, 111, 13], 'representative': 144, 'size': 1}
  • id: 142439353
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 108, 'group_counter': 10116, 'group_order': 960, 'label': '20A-3', 'order': 20, 'powers': [63, 112, 12], 'representative': 816, 'size': 1}
  • id: 142439354
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 109, 'group_counter': 10116, 'group_order': 960, 'label': '20A7', 'order': 20, 'powers': [63, 105, 13], 'representative': 336, 'size': 1}
  • id: 142439356
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 110, 'group_counter': 10116, 'group_order': 960, 'label': '20A-7', 'order': 20, 'powers': [64, 106, 12], 'representative': 624, 'size': 1}
  • id: 142439357
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 111, 'group_counter': 10116, 'group_order': 960, 'label': '20A9', 'order': 20, 'powers': [61, 109, 12], 'representative': 432, 'size': 1}
  • id: 142439358
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 112, 'group_counter': 10116, 'group_order': 960, 'label': '20A-9', 'order': 20, 'powers': [62, 110, 13], 'representative': 528, 'size': 1}
  • id: 142439359
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 113, 'group_counter': 10116, 'group_order': 960, 'label': '20B1', 'order': 20, 'powers': [62, 115, 14], 'representative': 56, 'size': 1}
  • id: 142439360
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 114, 'group_counter': 10116, 'group_order': 960, 'label': '20B-1', 'order': 20, 'powers': [61, 116, 15], 'representative': 920, 'size': 1}
  • id: 142439361
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 115, 'group_counter': 10116, 'group_order': 960, 'label': '20B3', 'order': 20, 'powers': [64, 119, 15], 'representative': 152, 'size': 1}
  • id: 142439362
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 116, 'group_counter': 10116, 'group_order': 960, 'label': '20B-3', 'order': 20, 'powers': [63, 120, 14], 'representative': 824, 'size': 1}
  • id: 142439363
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 117, 'group_counter': 10116, 'group_order': 960, 'label': '20B7', 'order': 20, 'powers': [63, 113, 15], 'representative': 344, 'size': 1}
  • id: 142439364
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 118, 'group_counter': 10116, 'group_order': 960, 'label': '20B-7', 'order': 20, 'powers': [64, 114, 14], 'representative': 632, 'size': 1}
  • id: 142439365
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 119, 'group_counter': 10116, 'group_order': 960, 'label': '20B9', 'order': 20, 'powers': [61, 117, 14], 'representative': 440, 'size': 1}
  • id: 142439367
    {'aut_label': '20A1', 'centralizer': '1.a1.a1', 'counter': 120, 'group_counter': 10116, 'group_order': 960, 'label': '20B-9', 'order': 20, 'powers': [62, 118, 15], 'representative': 536, 'size': 1}
  • id: 142439368
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 121, 'group_counter': 10116, 'group_order': 960, 'label': '20C1', 'order': 20, 'powers': [60, 123, 16], 'representative': 683, 'size': 2}
  • id: 142439369
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 122, 'group_counter': 10116, 'group_order': 960, 'label': '20C-1', 'order': 20, 'powers': [59, 124, 16], 'representative': 771, 'size': 2}
  • id: 142439370
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 123, 'group_counter': 10116, 'group_order': 960, 'label': '20C3', 'order': 20, 'powers': [57, 122, 16], 'representative': 579, 'size': 2}
  • id: 142439371
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 124, 'group_counter': 10116, 'group_order': 960, 'label': '20C-3', 'order': 20, 'powers': [58, 121, 16], 'representative': 875, 'size': 2}
  • id: 142439372
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 125, 'group_counter': 10116, 'group_order': 960, 'label': '20D1', 'order': 20, 'powers': [57, 127, 17], 'representative': 587, 'size': 2}
  • id: 142439373
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 126, 'group_counter': 10116, 'group_order': 960, 'label': '20D-1', 'order': 20, 'powers': [58, 128, 17], 'representative': 867, 'size': 2}
  • id: 142439374
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 127, 'group_counter': 10116, 'group_order': 960, 'label': '20D3', 'order': 20, 'powers': [59, 126, 17], 'representative': 291, 'size': 2}
  • id: 142439375
    {'aut_label': '20C1', 'centralizer': '2.h1.a1', 'counter': 128, 'group_counter': 10116, 'group_order': 960, 'label': '20D-3', 'order': 20, 'powers': [60, 125, 17], 'representative': 203, 'size': 2}
  • id: 142439376
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 129, 'group_counter': 10116, 'group_order': 960, 'label': '20E1', 'order': 20, 'powers': [62, 131, 18], 'representative': 50, 'size': 2}
  • id: 142439378
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 130, 'group_counter': 10116, 'group_order': 960, 'label': '20E-1', 'order': 20, 'powers': [61, 132, 19], 'representative': 914, 'size': 2}
  • id: 142439379
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 131, 'group_counter': 10116, 'group_order': 960, 'label': '20E3', 'order': 20, 'powers': [64, 135, 19], 'representative': 146, 'size': 2}
  • id: 142439380
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 132, 'group_counter': 10116, 'group_order': 960, 'label': '20E-3', 'order': 20, 'powers': [63, 136, 18], 'representative': 818, 'size': 2}
  • id: 142439381
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 133, 'group_counter': 10116, 'group_order': 960, 'label': '20E7', 'order': 20, 'powers': [63, 129, 19], 'representative': 338, 'size': 2}
  • id: 142439382
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 134, 'group_counter': 10116, 'group_order': 960, 'label': '20E-7', 'order': 20, 'powers': [64, 130, 18], 'representative': 626, 'size': 2}
  • id: 142439383
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 135, 'group_counter': 10116, 'group_order': 960, 'label': '20E9', 'order': 20, 'powers': [61, 133, 18], 'representative': 434, 'size': 2}
  • id: 142439384
    {'aut_label': '20E1', 'centralizer': '2.c1.a1', 'counter': 136, 'group_counter': 10116, 'group_order': 960, 'label': '20E-9', 'order': 20, 'powers': [62, 134, 19], 'representative': 530, 'size': 2}
  • id: 142439385
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 137, 'group_counter': 10116, 'group_order': 960, 'label': '20F1', 'order': 20, 'powers': [62, 139, 20], 'representative': 49, 'size': 2}
  • id: 142439386
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 138, 'group_counter': 10116, 'group_order': 960, 'label': '20F-1', 'order': 20, 'powers': [61, 140, 21], 'representative': 913, 'size': 2}
  • id: 142439387
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 139, 'group_counter': 10116, 'group_order': 960, 'label': '20F3', 'order': 20, 'powers': [64, 143, 21], 'representative': 145, 'size': 2}
  • id: 142439389
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 140, 'group_counter': 10116, 'group_order': 960, 'label': '20F-3', 'order': 20, 'powers': [63, 144, 20], 'representative': 817, 'size': 2}
  • id: 142439390
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 141, 'group_counter': 10116, 'group_order': 960, 'label': '20F7', 'order': 20, 'powers': [63, 137, 21], 'representative': 337, 'size': 2}
  • id: 142439391
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 142, 'group_counter': 10116, 'group_order': 960, 'label': '20F-7', 'order': 20, 'powers': [64, 138, 20], 'representative': 625, 'size': 2}
  • id: 142439392
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 143, 'group_counter': 10116, 'group_order': 960, 'label': '20F9', 'order': 20, 'powers': [61, 141, 20], 'representative': 433, 'size': 2}
  • id: 142439393
    {'aut_label': '20E1', 'centralizer': '2.c1.b1', 'counter': 144, 'group_counter': 10116, 'group_order': 960, 'label': '20F-9', 'order': 20, 'powers': [62, 142, 21], 'representative': 529, 'size': 2}
  • id: 142439394
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 145, 'group_counter': 10116, 'group_order': 960, 'label': '20G1', 'order': 20, 'powers': [54, 147, 22], 'representative': 539, 'size': 2}
  • id: 142439395
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 146, 'group_counter': 10116, 'group_order': 960, 'label': '20G-1', 'order': 20, 'powers': [53, 148, 23], 'representative': 915, 'size': 2}
  • id: 142439396
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 147, 'group_counter': 10116, 'group_order': 960, 'label': '20G3', 'order': 20, 'powers': [56, 151, 23], 'representative': 147, 'size': 2}
  • id: 142439397
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 148, 'group_counter': 10116, 'group_order': 960, 'label': '20G-3', 'order': 20, 'powers': [55, 152, 22], 'representative': 347, 'size': 2}
  • id: 142439398
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 149, 'group_counter': 10116, 'group_order': 960, 'label': '20G7', 'order': 20, 'powers': [55, 145, 23], 'representative': 339, 'size': 2}
  • id: 142439400
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 150, 'group_counter': 10116, 'group_order': 960, 'label': '20G-7', 'order': 20, 'powers': [56, 146, 22], 'representative': 155, 'size': 2}
  • id: 142439401
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 151, 'group_counter': 10116, 'group_order': 960, 'label': '20G9', 'order': 20, 'powers': [53, 149, 22], 'representative': 923, 'size': 2}
  • id: 142439402
    {'aut_label': '20G1', 'centralizer': '2.h1.a1', 'counter': 152, 'group_counter': 10116, 'group_order': 960, 'label': '20G-9', 'order': 20, 'powers': [54, 150, 23], 'representative': 531, 'size': 2}
  • id: 142439403
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 153, 'group_counter': 10116, 'group_order': 960, 'label': '20H1', 'order': 20, 'powers': [53, 155, 24], 'representative': 196, 'size': 3}
  • id: 142439404
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 154, 'group_counter': 10116, 'group_order': 960, 'label': '20H-1', 'order': 20, 'powers': [54, 156, 25], 'representative': 140, 'size': 3}
  • id: 142439405
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 155, 'group_counter': 10116, 'group_order': 960, 'label': '20H3', 'order': 20, 'powers': [55, 159, 25], 'representative': 588, 'size': 3}
  • id: 142439406
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 156, 'group_counter': 10116, 'group_order': 960, 'label': '20H-3', 'order': 20, 'powers': [56, 160, 24], 'representative': 68, 'size': 3}
  • id: 142439407
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 157, 'group_counter': 10116, 'group_order': 960, 'label': '20H7', 'order': 20, 'powers': [56, 153, 25], 'representative': 76, 'size': 3}
  • id: 142439408
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 158, 'group_counter': 10116, 'group_order': 960, 'label': '20H-7', 'order': 20, 'powers': [55, 154, 24], 'representative': 580, 'size': 3}
  • id: 142439409
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 159, 'group_counter': 10116, 'group_order': 960, 'label': '20H9', 'order': 20, 'powers': [54, 157, 24], 'representative': 132, 'size': 3}
  • id: 142439411
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 160, 'group_counter': 10116, 'group_order': 960, 'label': '20H-9', 'order': 20, 'powers': [53, 158, 25], 'representative': 204, 'size': 3}
  • id: 142439412
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 161, 'group_counter': 10116, 'group_order': 960, 'label': '20I1', 'order': 20, 'powers': [53, 163, 26], 'representative': 36, 'size': 3}
  • id: 142439413
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 162, 'group_counter': 10116, 'group_order': 960, 'label': '20I-1', 'order': 20, 'powers': [54, 164, 27], 'representative': 620, 'size': 3}
  • id: 142439414
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 163, 'group_counter': 10116, 'group_order': 960, 'label': '20I3', 'order': 20, 'powers': [55, 167, 27], 'representative': 108, 'size': 3}
  • id: 142439415
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 164, 'group_counter': 10116, 'group_order': 960, 'label': '20I-3', 'order': 20, 'powers': [56, 168, 26], 'representative': 228, 'size': 3}
  • id: 142439416
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 165, 'group_counter': 10116, 'group_order': 960, 'label': '20I7', 'order': 20, 'powers': [56, 161, 27], 'representative': 236, 'size': 3}
  • id: 142439417
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 166, 'group_counter': 10116, 'group_order': 960, 'label': '20I-7', 'order': 20, 'powers': [55, 162, 26], 'representative': 100, 'size': 3}
  • id: 142439418
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 167, 'group_counter': 10116, 'group_order': 960, 'label': '20I9', 'order': 20, 'powers': [54, 165, 26], 'representative': 612, 'size': 3}
  • id: 142439419
    {'aut_label': '20H1', 'centralizer': '3.a1.a1', 'counter': 168, 'group_counter': 10116, 'group_order': 960, 'label': '20I-9', 'order': 20, 'powers': [53, 166, 27], 'representative': 44, 'size': 3}
  • id: 142439420
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 169, 'group_counter': 10116, 'group_order': 960, 'label': '20J1', 'order': 20, 'powers': [57, 171, 28], 'representative': 20, 'size': 3}
  • id: 142439422
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 170, 'group_counter': 10116, 'group_order': 960, 'label': '20J-1', 'order': 20, 'powers': [58, 172, 29], 'representative': 636, 'size': 3}
  • id: 142439423
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 171, 'group_counter': 10116, 'group_order': 960, 'label': '20J3', 'order': 20, 'powers': [59, 175, 29], 'representative': 60, 'size': 3}
  • id: 142439424
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 172, 'group_counter': 10116, 'group_order': 960, 'label': '20J-3', 'order': 20, 'powers': [60, 176, 28], 'representative': 596, 'size': 3}
  • id: 142439425
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 173, 'group_counter': 10116, 'group_order': 960, 'label': '20J7', 'order': 20, 'powers': [60, 169, 29], 'representative': 124, 'size': 3}
  • id: 142439426
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 174, 'group_counter': 10116, 'group_order': 960, 'label': '20J-7', 'order': 20, 'powers': [59, 170, 28], 'representative': 212, 'size': 3}
  • id: 142439427
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 175, 'group_counter': 10116, 'group_order': 960, 'label': '20J9', 'order': 20, 'powers': [58, 173, 28], 'representative': 148, 'size': 3}
  • id: 142439428
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 176, 'group_counter': 10116, 'group_order': 960, 'label': '20J-9', 'order': 20, 'powers': [57, 174, 29], 'representative': 188, 'size': 3}
  • id: 142439429
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 177, 'group_counter': 10116, 'group_order': 960, 'label': '20K1', 'order': 20, 'powers': [59, 179, 30], 'representative': 52, 'size': 3}
  • id: 142439430
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 178, 'group_counter': 10116, 'group_order': 960, 'label': '20K-1', 'order': 20, 'powers': [60, 180, 31], 'representative': 604, 'size': 3}
  • id: 142439431
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 179, 'group_counter': 10116, 'group_order': 960, 'label': '20K3', 'order': 20, 'powers': [58, 183, 31], 'representative': 156, 'size': 3}
  • id: 142439433
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 180, 'group_counter': 10116, 'group_order': 960, 'label': '20K-3', 'order': 20, 'powers': [57, 184, 30], 'representative': 180, 'size': 3}
  • id: 142439434
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 181, 'group_counter': 10116, 'group_order': 960, 'label': '20K7', 'order': 20, 'powers': [57, 177, 31], 'representative': 28, 'size': 3}
  • id: 142439435
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 182, 'group_counter': 10116, 'group_order': 960, 'label': '20K-7', 'order': 20, 'powers': [58, 178, 30], 'representative': 628, 'size': 3}
  • id: 142439436
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 183, 'group_counter': 10116, 'group_order': 960, 'label': '20K9', 'order': 20, 'powers': [60, 181, 30], 'representative': 116, 'size': 3}
  • id: 142439437
    {'aut_label': '20J1', 'centralizer': '3.a1.a1', 'counter': 184, 'group_counter': 10116, 'group_order': 960, 'label': '20K-9', 'order': 20, 'powers': [59, 182, 31], 'representative': 220, 'size': 3}
  • id: 142439438
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 185, 'group_counter': 10116, 'group_order': 960, 'label': '20L1', 'order': 20, 'powers': [57, 187, 32], 'representative': 22, 'size': 6}
  • id: 142439439
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 186, 'group_counter': 10116, 'group_order': 960, 'label': '20L-1', 'order': 20, 'powers': [58, 188, 32], 'representative': 150, 'size': 6}
  • id: 142439440
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 187, 'group_counter': 10116, 'group_order': 960, 'label': '20L3', 'order': 20, 'powers': [59, 186, 32], 'representative': 214, 'size': 6}
  • id: 142439441
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 188, 'group_counter': 10116, 'group_order': 960, 'label': '20L-3', 'order': 20, 'powers': [60, 185, 32], 'representative': 598, 'size': 6}
  • id: 142439442
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 189, 'group_counter': 10116, 'group_order': 960, 'label': '20M1', 'order': 20, 'powers': [57, 191, 33], 'representative': 21, 'size': 6}
  • id: 142439444
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 190, 'group_counter': 10116, 'group_order': 960, 'label': '20M-1', 'order': 20, 'powers': [58, 192, 33], 'representative': 149, 'size': 6}
  • id: 142439445
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 191, 'group_counter': 10116, 'group_order': 960, 'label': '20M3', 'order': 20, 'powers': [59, 190, 33], 'representative': 213, 'size': 6}
  • id: 142439446
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 192, 'group_counter': 10116, 'group_order': 960, 'label': '20M-3', 'order': 20, 'powers': [60, 189, 33], 'representative': 597, 'size': 6}
  • id: 142439447
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 193, 'group_counter': 10116, 'group_order': 960, 'label': '20N1', 'order': 20, 'powers': [59, 195, 34], 'representative': 54, 'size': 6}
  • id: 142439448
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 194, 'group_counter': 10116, 'group_order': 960, 'label': '20N-1', 'order': 20, 'powers': [60, 196, 34], 'representative': 118, 'size': 6}
  • id: 142439449
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 195, 'group_counter': 10116, 'group_order': 960, 'label': '20N3', 'order': 20, 'powers': [58, 194, 34], 'representative': 158, 'size': 6}
  • id: 142439450
    {'aut_label': '20L1', 'centralizer': '6.d1.a1', 'counter': 196, 'group_counter': 10116, 'group_order': 960, 'label': '20N-3', 'order': 20, 'powers': [57, 193, 34], 'representative': 30, 'size': 6}
  • id: 142439451
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 197, 'group_counter': 10116, 'group_order': 960, 'label': '20O1', 'order': 20, 'powers': [59, 199, 35], 'representative': 53, 'size': 6}
  • id: 142439452
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 198, 'group_counter': 10116, 'group_order': 960, 'label': '20O-1', 'order': 20, 'powers': [60, 200, 35], 'representative': 117, 'size': 6}
  • id: 142439453
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 199, 'group_counter': 10116, 'group_order': 960, 'label': '20O3', 'order': 20, 'powers': [58, 198, 35], 'representative': 157, 'size': 6}
  • id: 142439456
    {'aut_label': '20L1', 'centralizer': '6.d1.b1', 'counter': 200, 'group_counter': 10116, 'group_order': 960, 'label': '20O-3', 'order': 20, 'powers': [57, 197, 35], 'representative': 29, 'size': 6}
  • id: 142439457
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 201, 'group_counter': 10116, 'group_order': 960, 'label': '20P1', 'order': 20, 'powers': [53, 203, 36], 'representative': 198, 'size': 6}
  • id: 142439458
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 202, 'group_counter': 10116, 'group_order': 960, 'label': '20P-1', 'order': 20, 'powers': [54, 204, 37], 'representative': 142, 'size': 6}
  • id: 142439459
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 203, 'group_counter': 10116, 'group_order': 960, 'label': '20P3', 'order': 20, 'powers': [55, 207, 37], 'representative': 102, 'size': 6}
  • id: 142439460
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 204, 'group_counter': 10116, 'group_order': 960, 'label': '20P-3', 'order': 20, 'powers': [56, 208, 36], 'representative': 70, 'size': 6}
  • id: 142439461
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 205, 'group_counter': 10116, 'group_order': 960, 'label': '20P7', 'order': 20, 'powers': [56, 201, 37], 'representative': 230, 'size': 6}
  • id: 142439462
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 206, 'group_counter': 10116, 'group_order': 960, 'label': '20P-7', 'order': 20, 'powers': [55, 202, 36], 'representative': 582, 'size': 6}
  • id: 142439463
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 207, 'group_counter': 10116, 'group_order': 960, 'label': '20P9', 'order': 20, 'powers': [54, 205, 36], 'representative': 134, 'size': 6}
  • id: 142439464
    {'aut_label': '20P1', 'centralizer': '6.d1.a1', 'counter': 208, 'group_counter': 10116, 'group_order': 960, 'label': '20P-9', 'order': 20, 'powers': [53, 206, 37], 'representative': 38, 'size': 6}
  • id: 142439465
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 209, 'group_counter': 10116, 'group_order': 960, 'label': '20Q1', 'order': 20, 'powers': [53, 211, 38], 'representative': 197, 'size': 6}
  • id: 142439467
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 210, 'group_counter': 10116, 'group_order': 960, 'label': '20Q-1', 'order': 20, 'powers': [54, 212, 39], 'representative': 141, 'size': 6}
  • id: 142439468
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 211, 'group_counter': 10116, 'group_order': 960, 'label': '20Q3', 'order': 20, 'powers': [55, 215, 39], 'representative': 101, 'size': 6}
  • id: 142439469
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 212, 'group_counter': 10116, 'group_order': 960, 'label': '20Q-3', 'order': 20, 'powers': [56, 216, 38], 'representative': 69, 'size': 6}
  • id: 142439470
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 213, 'group_counter': 10116, 'group_order': 960, 'label': '20Q7', 'order': 20, 'powers': [56, 209, 39], 'representative': 229, 'size': 6}
  • id: 142439471
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 214, 'group_counter': 10116, 'group_order': 960, 'label': '20Q-7', 'order': 20, 'powers': [55, 210, 38], 'representative': 581, 'size': 6}
  • id: 142439472
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 215, 'group_counter': 10116, 'group_order': 960, 'label': '20Q9', 'order': 20, 'powers': [54, 213, 38], 'representative': 133, 'size': 6}
  • id: 142439473
    {'aut_label': '20P1', 'centralizer': '6.d1.b1', 'counter': 216, 'group_counter': 10116, 'group_order': 960, 'label': '20Q-9', 'order': 20, 'powers': [53, 214, 39], 'representative': 37, 'size': 6}
  • id: 142439474
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 217, 'group_counter': 10116, 'group_order': 960, 'label': '20R1', 'order': 20, 'powers': [61, 219, 40], 'representative': 199, 'size': 6}
  • id: 142439475
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 218, 'group_counter': 10116, 'group_order': 960, 'label': '20R-1', 'order': 20, 'powers': [62, 220, 41], 'representative': 143, 'size': 6}
  • id: 142439476
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 219, 'group_counter': 10116, 'group_order': 960, 'label': '20R3', 'order': 20, 'powers': [63, 223, 41], 'representative': 103, 'size': 6}
  • id: 142439478
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 220, 'group_counter': 10116, 'group_order': 960, 'label': '20R-3', 'order': 20, 'powers': [64, 224, 40], 'representative': 71, 'size': 6}
  • id: 142439479
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 221, 'group_counter': 10116, 'group_order': 960, 'label': '20R7', 'order': 20, 'powers': [64, 217, 41], 'representative': 231, 'size': 6}
  • id: 142439480
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 222, 'group_counter': 10116, 'group_order': 960, 'label': '20R-7', 'order': 20, 'powers': [63, 218, 40], 'representative': 583, 'size': 6}
  • id: 142439481
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 223, 'group_counter': 10116, 'group_order': 960, 'label': '20R9', 'order': 20, 'powers': [62, 221, 40], 'representative': 135, 'size': 6}
  • id: 142439482
    {'aut_label': '20R1', 'centralizer': '6.h1.a1', 'counter': 224, 'group_counter': 10116, 'group_order': 960, 'label': '20R-9', 'order': 20, 'powers': [61, 222, 41], 'representative': 39, 'size': 6}
  • id: 142439483
    {'aut_label': '30A1', 'centralizer': '2.f1.a1', 'counter': 225, 'group_counter': 10116, 'group_order': 960, 'label': '30A1', 'order': 30, 'powers': [104, 62, 46], 'representative': 32, 'size': 2}
  • id: 142439484
    {'aut_label': '30A1', 'centralizer': '2.f1.a1', 'counter': 226, 'group_counter': 10116, 'group_order': 960, 'label': '30A-1', 'order': 30, 'powers': [103, 61, 46], 'representative': 928, 'size': 2}
  • id: 142439485
    {'aut_label': '30A1', 'centralizer': '2.f1.a1', 'counter': 227, 'group_counter': 10116, 'group_order': 960, 'label': '30A7', 'order': 30, 'powers': [101, 63, 46], 'representative': 224, 'size': 2}
  • id: 142439486
    {'aut_label': '30A1', 'centralizer': '2.f1.a1', 'counter': 228, 'group_counter': 10116, 'group_order': 960, 'label': '30A-7', 'order': 30, 'powers': [102, 64, 46], 'representative': 736, 'size': 2}
  • id: 142439487
    {'aut_label': '30B1', 'centralizer': '2.f1.a1', 'counter': 229, 'group_counter': 10116, 'group_order': 960, 'label': '30B1', 'order': 30, 'powers': [103, 60, 47], 'representative': 616, 'size': 2}
  • id: 142439489
    {'aut_label': '30B1', 'centralizer': '2.f1.a1', 'counter': 230, 'group_counter': 10116, 'group_order': 960, 'label': '30B-1', 'order': 30, 'powers': [104, 59, 47], 'representative': 360, 'size': 2}
  • id: 142439490
    {'aut_label': '30B1', 'centralizer': '2.f1.a1', 'counter': 231, 'group_counter': 10116, 'group_order': 960, 'label': '30B7', 'order': 30, 'powers': [102, 58, 47], 'representative': 424, 'size': 2}
  • id: 142439491
    {'aut_label': '30B1', 'centralizer': '2.f1.a1', 'counter': 232, 'group_counter': 10116, 'group_order': 960, 'label': '30B-7', 'order': 30, 'powers': [101, 57, 47], 'representative': 552, 'size': 2}
  • id: 142439492
    {'aut_label': '30C1', 'centralizer': '2.f1.a1', 'counter': 233, 'group_counter': 10116, 'group_order': 960, 'label': '30C1', 'order': 30, 'powers': [104, 54, 48], 'representative': 520, 'size': 2}
  • id: 142439493
    {'aut_label': '30C1', 'centralizer': '2.f1.a1', 'counter': 234, 'group_counter': 10116, 'group_order': 960, 'label': '30C-1', 'order': 30, 'powers': [103, 53, 48], 'representative': 456, 'size': 2}
  • id: 142439494
    {'aut_label': '30C1', 'centralizer': '2.f1.a1', 'counter': 235, 'group_counter': 10116, 'group_order': 960, 'label': '30C7', 'order': 30, 'powers': [101, 55, 48], 'representative': 712, 'size': 2}
  • id: 142439495
    {'aut_label': '30C1', 'centralizer': '2.f1.a1', 'counter': 236, 'group_counter': 10116, 'group_order': 960, 'label': '30C-7', 'order': 30, 'powers': [102, 56, 48], 'representative': 264, 'size': 2}
  • id: 142439496
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 237, 'group_counter': 10116, 'group_order': 960, 'label': '30D1', 'order': 30, 'powers': [101, 65, 49], 'representative': 66, 'size': 4}
  • id: 142439497
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 238, 'group_counter': 10116, 'group_order': 960, 'label': '30D-1', 'order': 30, 'powers': [102, 66, 49], 'representative': 258, 'size': 4}
  • id: 142439498
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 239, 'group_counter': 10116, 'group_order': 960, 'label': '30D7', 'order': 30, 'powers': [103, 68, 49], 'representative': 130, 'size': 4}
  • id: 142439500
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 240, 'group_counter': 10116, 'group_order': 960, 'label': '30D-7', 'order': 30, 'powers': [104, 67, 49], 'representative': 42, 'size': 4}
  • id: 142439501
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 241, 'group_counter': 10116, 'group_order': 960, 'label': '30E1', 'order': 30, 'powers': [104, 69, 50], 'representative': 34, 'size': 4}
  • id: 142439502
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 242, 'group_counter': 10116, 'group_order': 960, 'label': '30E-1', 'order': 30, 'powers': [103, 70, 50], 'representative': 138, 'size': 4}
  • id: 142439503
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 243, 'group_counter': 10116, 'group_order': 960, 'label': '30E7', 'order': 30, 'powers': [101, 72, 50], 'representative': 226, 'size': 4}
  • id: 142439504
    {'aut_label': '30D1', 'centralizer': '4.b1.a1', 'counter': 244, 'group_counter': 10116, 'group_order': 960, 'label': '30E-7', 'order': 30, 'powers': [102, 71, 50], 'representative': 418, 'size': 4}
  • id: 142439505
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 245, 'group_counter': 10116, 'group_order': 960, 'label': '30F1', 'order': 30, 'powers': [101, 73, 51], 'representative': 65, 'size': 4}
  • id: 142439506
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 246, 'group_counter': 10116, 'group_order': 960, 'label': '30F-1', 'order': 30, 'powers': [102, 74, 51], 'representative': 257, 'size': 4}
  • id: 142439507
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 247, 'group_counter': 10116, 'group_order': 960, 'label': '30F7', 'order': 30, 'powers': [103, 76, 51], 'representative': 129, 'size': 4}
  • id: 142439508
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 248, 'group_counter': 10116, 'group_order': 960, 'label': '30F-7', 'order': 30, 'powers': [104, 75, 51], 'representative': 41, 'size': 4}
  • id: 142439509
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 249, 'group_counter': 10116, 'group_order': 960, 'label': '30G1', 'order': 30, 'powers': [104, 77, 52], 'representative': 33, 'size': 4}
  • id: 142439511
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 250, 'group_counter': 10116, 'group_order': 960, 'label': '30G-1', 'order': 30, 'powers': [103, 78, 52], 'representative': 137, 'size': 4}
  • id: 142439512
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 251, 'group_counter': 10116, 'group_order': 960, 'label': '30G7', 'order': 30, 'powers': [101, 80, 52], 'representative': 225, 'size': 4}
  • id: 142439513
    {'aut_label': '30D1', 'centralizer': '4.b1.b1', 'counter': 252, 'group_counter': 10116, 'group_order': 960, 'label': '30G-7', 'order': 30, 'powers': [102, 79, 52], 'representative': 417, 'size': 4}
  • id: 142439514
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 253, 'group_counter': 10116, 'group_order': 960, 'label': '60A1', 'order': 60, 'powers': [225, 105, 89], 'representative': 16, 'size': 2}
  • id: 142439515
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 254, 'group_counter': 10116, 'group_order': 960, 'label': '60A-1', 'order': 60, 'powers': [226, 106, 90], 'representative': 304, 'size': 2}
  • id: 142439516
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 255, 'group_counter': 10116, 'group_order': 960, 'label': '60A7', 'order': 60, 'powers': [227, 109, 90], 'representative': 112, 'size': 2}
  • id: 142439517
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 256, 'group_counter': 10116, 'group_order': 960, 'label': '60A-7', 'order': 60, 'powers': [228, 110, 89], 'representative': 208, 'size': 2}
  • id: 142439518
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 257, 'group_counter': 10116, 'group_order': 960, 'label': '60A11', 'order': 60, 'powers': [225, 112, 90], 'representative': 176, 'size': 2}
  • id: 142439519
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 258, 'group_counter': 10116, 'group_order': 960, 'label': '60A-11', 'order': 60, 'powers': [226, 111, 89], 'representative': 784, 'size': 2}
  • id: 142439520
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 259, 'group_counter': 10116, 'group_order': 960, 'label': '60A17', 'order': 60, 'powers': [227, 108, 89], 'representative': 592, 'size': 2}
  • id: 142439522
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 260, 'group_counter': 10116, 'group_order': 960, 'label': '60A-17', 'order': 60, 'powers': [228, 107, 90], 'representative': 368, 'size': 2}
  • id: 142439523
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 261, 'group_counter': 10116, 'group_order': 960, 'label': '60B1', 'order': 60, 'powers': [225, 113, 91], 'representative': 24, 'size': 2}
  • id: 142439524
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 262, 'group_counter': 10116, 'group_order': 960, 'label': '60B-1', 'order': 60, 'powers': [226, 114, 92], 'representative': 312, 'size': 2}
  • id: 142439525
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 263, 'group_counter': 10116, 'group_order': 960, 'label': '60B7', 'order': 60, 'powers': [227, 117, 92], 'representative': 120, 'size': 2}
  • id: 142439526
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 264, 'group_counter': 10116, 'group_order': 960, 'label': '60B-7', 'order': 60, 'powers': [228, 118, 91], 'representative': 216, 'size': 2}
  • id: 142439527
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 265, 'group_counter': 10116, 'group_order': 960, 'label': '60B11', 'order': 60, 'powers': [225, 120, 92], 'representative': 184, 'size': 2}
  • id: 142439528
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 266, 'group_counter': 10116, 'group_order': 960, 'label': '60B-11', 'order': 60, 'powers': [226, 119, 91], 'representative': 792, 'size': 2}
  • id: 142439529
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 267, 'group_counter': 10116, 'group_order': 960, 'label': '60B17', 'order': 60, 'powers': [227, 116, 91], 'representative': 600, 'size': 2}
  • id: 142439530
    {'aut_label': '60A1', 'centralizer': '2.f1.a1', 'counter': 268, 'group_counter': 10116, 'group_order': 960, 'label': '60B-17', 'order': 60, 'powers': [228, 115, 92], 'representative': 376, 'size': 2}
  • id: 142439531
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 269, 'group_counter': 10116, 'group_order': 960, 'label': '60C1', 'order': 60, 'powers': [229, 121, 93], 'representative': 67, 'size': 4}
  • id: 142439533
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 270, 'group_counter': 10116, 'group_order': 960, 'label': '60C-1', 'order': 60, 'powers': [230, 122, 93], 'representative': 259, 'size': 4}
  • id: 142439534
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 271, 'group_counter': 10116, 'group_order': 960, 'label': '60C7', 'order': 60, 'powers': [231, 124, 93], 'representative': 131, 'size': 4}
  • id: 142439535
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 272, 'group_counter': 10116, 'group_order': 960, 'label': '60C-7', 'order': 60, 'powers': [232, 123, 93], 'representative': 43, 'size': 4}
  • id: 142439536
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 273, 'group_counter': 10116, 'group_order': 960, 'label': '60D1', 'order': 60, 'powers': [232, 125, 94], 'representative': 35, 'size': 4}
  • id: 142439537
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 274, 'group_counter': 10116, 'group_order': 960, 'label': '60D-1', 'order': 60, 'powers': [231, 126, 94], 'representative': 139, 'size': 4}
  • id: 142439538
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 275, 'group_counter': 10116, 'group_order': 960, 'label': '60D7', 'order': 60, 'powers': [229, 128, 94], 'representative': 227, 'size': 4}
  • id: 142439539
    {'aut_label': '60C1', 'centralizer': '4.l1.a1', 'counter': 276, 'group_counter': 10116, 'group_order': 960, 'label': '60D-7', 'order': 60, 'powers': [230, 127, 94], 'representative': 419, 'size': 4}
  • id: 142439540
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 277, 'group_counter': 10116, 'group_order': 960, 'label': '60E1', 'order': 60, 'powers': [225, 129, 95], 'representative': 18, 'size': 4}
  • id: 142439541
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 278, 'group_counter': 10116, 'group_order': 960, 'label': '60E-1', 'order': 60, 'powers': [226, 130, 96], 'representative': 794, 'size': 4}
  • id: 142439542
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 279, 'group_counter': 10116, 'group_order': 960, 'label': '60E7', 'order': 60, 'powers': [227, 133, 96], 'representative': 114, 'size': 4}
  • id: 142439544
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 280, 'group_counter': 10116, 'group_order': 960, 'label': '60E-7', 'order': 60, 'powers': [228, 134, 95], 'representative': 210, 'size': 4}
  • id: 142439545
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 281, 'group_counter': 10116, 'group_order': 960, 'label': '60E11', 'order': 60, 'powers': [225, 136, 96], 'representative': 26, 'size': 4}
  • id: 142439546
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 282, 'group_counter': 10116, 'group_order': 960, 'label': '60E-11', 'order': 60, 'powers': [226, 135, 95], 'representative': 786, 'size': 4}
  • id: 142439547
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 283, 'group_counter': 10116, 'group_order': 960, 'label': '60E17', 'order': 60, 'powers': [227, 132, 95], 'representative': 594, 'size': 4}
  • id: 142439548
    {'aut_label': '60E1', 'centralizer': '4.b1.a1', 'counter': 284, 'group_counter': 10116, 'group_order': 960, 'label': '60E-17', 'order': 60, 'powers': [228, 131, 96], 'representative': 218, 'size': 4}
  • id: 142439549
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 285, 'group_counter': 10116, 'group_order': 960, 'label': '60F1', 'order': 60, 'powers': [225, 137, 97], 'representative': 17, 'size': 4}
  • id: 142439550
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 286, 'group_counter': 10116, 'group_order': 960, 'label': '60F-1', 'order': 60, 'powers': [226, 138, 98], 'representative': 793, 'size': 4}
  • id: 142439551
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 287, 'group_counter': 10116, 'group_order': 960, 'label': '60F7', 'order': 60, 'powers': [227, 141, 98], 'representative': 113, 'size': 4}
  • id: 142439552
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 288, 'group_counter': 10116, 'group_order': 960, 'label': '60F-7', 'order': 60, 'powers': [228, 142, 97], 'representative': 209, 'size': 4}
  • id: 142439553
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 289, 'group_counter': 10116, 'group_order': 960, 'label': '60F11', 'order': 60, 'powers': [225, 144, 98], 'representative': 25, 'size': 4}
  • id: 142439555
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 290, 'group_counter': 10116, 'group_order': 960, 'label': '60F-11', 'order': 60, 'powers': [226, 143, 97], 'representative': 785, 'size': 4}
  • id: 142439556
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 291, 'group_counter': 10116, 'group_order': 960, 'label': '60F17', 'order': 60, 'powers': [227, 140, 97], 'representative': 593, 'size': 4}
  • id: 142439557
    {'aut_label': '60E1', 'centralizer': '4.b1.b1', 'counter': 292, 'group_counter': 10116, 'group_order': 960, 'label': '60F-17', 'order': 60, 'powers': [228, 139, 98], 'representative': 217, 'size': 4}
  • id: 142439558
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 293, 'group_counter': 10116, 'group_order': 960, 'label': '60G1', 'order': 60, 'powers': [233, 145, 99], 'representative': 19, 'size': 4}
  • id: 142439559
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 294, 'group_counter': 10116, 'group_order': 960, 'label': '60G-1', 'order': 60, 'powers': [234, 146, 100], 'representative': 795, 'size': 4}
  • id: 142439560
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 295, 'group_counter': 10116, 'group_order': 960, 'label': '60G7', 'order': 60, 'powers': [235, 149, 100], 'representative': 115, 'size': 4}
  • id: 142439561
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 296, 'group_counter': 10116, 'group_order': 960, 'label': '60G-7', 'order': 60, 'powers': [236, 150, 99], 'representative': 211, 'size': 4}
  • id: 142439562
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 297, 'group_counter': 10116, 'group_order': 960, 'label': '60G11', 'order': 60, 'powers': [233, 152, 100], 'representative': 27, 'size': 4}
  • id: 142439563
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 298, 'group_counter': 10116, 'group_order': 960, 'label': '60G-11', 'order': 60, 'powers': [234, 151, 99], 'representative': 787, 'size': 4}
  • id: 142439564
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 299, 'group_counter': 10116, 'group_order': 960, 'label': '60G17', 'order': 60, 'powers': [235, 148, 99], 'representative': 595, 'size': 4}
  • id: 142439567
    {'aut_label': '60G1', 'centralizer': '4.l1.a1', 'counter': 300, 'group_counter': 10116, 'group_order': 960, 'label': '60G-17', 'order': 60, 'powers': [236, 147, 100], 'representative': 219, 'size': 4}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 13389803
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1a', '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], 'schur_index': 1}
  • id: 13389814
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -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: 13389825
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 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: 13389836
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -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: 13389847
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 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: 13389858
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 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: 13389869
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -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: 13389880
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  • id: 13389888
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  • id: 13389804
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  • id: 13389805
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  • id: 13389806
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  • id: 13389807
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  • id: 13389808
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  • id: 13389809
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 13389810
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -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: 13389811
    {'cdim': 1, 'counter': 17, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1q', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, -2, 0, 0, -2, 0, 0, 2, 0, 0, -2, 2, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, 2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389812
    {'cdim': 1, 'counter': 18, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1r', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 2, 0, 0, 2, 0, 0, -2, 0, 0, 2, -2, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, -2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389813
    {'cdim': 1, 'counter': 19, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1s', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 2, 0, 0, 2, 0, 0, 2, 0, 0, -2, -2, 0, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, 2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389815
    {'cdim': 1, 'counter': 20, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1t', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, -2, 0, 0, -2, 0, 0, -2, 0, 0, 2, 2, 0, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, -2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389816
    {'cdim': 1, 'counter': 21, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1u', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 2, 0, 0, -2, 0, 0, -2, 0, 0, 2, 2, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, -2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389817
    {'cdim': 1, 'counter': 22, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1v', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, -2, 0, 0, 2, 0, 0, 2, 0, 0, -2, -2, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, 2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389818
    {'cdim': 1, 'counter': 23, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1w', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 2, -2, 0, 0, 2, 0, 0, -2, 0, 0, 2, -2, 0, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, -2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389819
    {'cdim': 1, 'counter': 24, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1x', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 0, -2, 2, 0, 0, -2, 0, 0, 2, 0, 0, -2, 2, 0, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, 2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389846
    {'cdim': 2, 'counter': 49, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 13389848
    {'cdim': 2, 'counter': 50, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, -1, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 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: 13389849
    {'cdim': 2, 'counter': 51, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, 0, -1, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -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: 13389850
    {'cdim': 2, 'counter': 52, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, -1, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -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: 13389851
    {'cdim': 2, 'counter': 53, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, 0, -1, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 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: 13389852
    {'cdim': 2, 'counter': 54, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 0, 0, -1, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -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: 13389853
    {'cdim': 2, 'counter': 55, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 0, 0, -1, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 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: 13389854
    {'cdim': 2, 'counter': 56, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 13389820
    {'cdim': 1, 'counter': 25, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1y', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 13389821
    {'cdim': 1, 'counter': 26, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1z', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 4, -4, 4, 4, -4, -1, -1, -1, -1, 4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, 4, 4, 4, 4, -4, 4, -4, 4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 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: 13389822
    {'cdim': 1, 'counter': 27, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1aa', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, 4, 4, -4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, -4, -4, 4, 4, 4, -4, 4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -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: 13389823
    {'cdim': 1, 'counter': 28, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ab', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, -4, 4, -4, -4, 4, -4, 4, -4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, 4, -1, -1, -1, -1, 4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, 4, 4, 4, 4, -4, 4, -4, 4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 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: 13389824
    {'cdim': 1, 'counter': 29, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ac', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, -4, -4, -4, -4, -1, -1, -1, -1, 4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, -4, -4, 4, 4, 4, -4, 4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -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: 13389826
    {'cdim': 1, 'counter': 30, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ad', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, 4, -4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, 4, -4, -4, -4, 4, 4, 4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -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: 13389827
    {'cdim': 1, 'counter': 31, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ae', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 4, 4, -4, 4, -4, -4, 4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, 4, 4, -4, 4, 4, -4, -4, -1, -1, -1, -1, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, -4, 4, -4, -4, -4, -4, -4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 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: 13389828
    {'cdim': 1, 'counter': 32, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1af', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 4, 4, -4, 4, -4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, -4, 4, -4, -1, -1, -1, -1, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, 4, -4, -4, -4, 4, 4, 4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -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: 13389829
    {'cdim': 1, 'counter': 33, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ag', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, 4, -4, -4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, 4, -4, -4, 4, -4, -4, 4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, -4, 4, -4, -4, -4, -4, -4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 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: 13389830
    {'cdim': 1, 'counter': 34, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ah', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, -4, 4, -4, 4, -4, 4, -4, 4, 4, -4, 4, 4, -4, 4, -4, 4, 4, -4, 4, -4, -1, -1, -1, -1, 4, 4, 4, -4, -4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, 4, -4, -4, 4, -4, 4, 4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -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: 13389831
    {'cdim': 1, 'counter': 35, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ai', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, -4, 4, -4, 4, 4, 4, 4, 4, 4, 4, 4, -4, 4, 4, -4, -4, -4, -4, -4, 4, 4, -1, -1, -1, -1, 4, 4, 4, -4, -4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 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: 13389832
    {'cdim': 1, 'counter': 36, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1aj', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, 4, 4, 4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, -4, 4, 4, -4, 4, -4, 4, -4, -4, 4, -4, -4, 4, -4, 4, -4, -4, 4, -4, 4, -1, -1, -1, -1, 4, 4, 4, -4, -4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, 4, -4, -4, 4, -4, 4, 4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -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: 13389833
    {'cdim': 1, 'counter': 37, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ak', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, -4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, 4, 4, 4, -4, -4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 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: 13389834
    {'cdim': 1, 'counter': 38, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1al', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, -4, -4, 4, -4, -4, 4, -4, -4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, -4, 4, 4, -4, 4, 4, -4, -4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 13389835
    {'cdim': 1, 'counter': 39, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1am', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 13389837
    {'cdim': 1, 'counter': 40, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1an', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, -4, -4, 4, -4, -4, -4, -4, -4, 4, -4, 4, -4, 4, 4, -4, -4, 4, -4, -4, 4, -4, -4, 4, 4, -4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, -4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 13389855
    {'cdim': 2, 'counter': 57, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2i', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -4, -4, 0, -4, 0, -4, -4, 4, 4, 4, -4, -4, 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 13389856
    {'cdim': 2, 'counter': 58, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2j', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 4, 4, 0, 4, 0, 4, 4, -4, -4, -4, 4, 4, 0, 0, -4, -4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 13389857
    {'cdim': 2, 'counter': 59, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2k', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, 4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, -4, -4, -4, 4, 4, -4, 4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13389859
    {'cdim': 2, 'counter': 60, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2l', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, 4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13389860
    {'cdim': 2, 'counter': 61, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2m', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, -4, 4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 2, -2, 2, 2, -2, 2, -2, -4, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, -4, 4, 4, -4, -4, 4, -4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389861
    {'cdim': 2, 'counter': 62, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2n', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 4, -4, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 2, -2, 2, -2, 2, 2, -2, -4, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, -4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, -4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389862
    {'cdim': 2, 'counter': 63, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2o', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 2, -2, 2, 2, -2, -2, 2, -4, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, -4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389863
    {'cdim': 2, 'counter': 64, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2p', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 2, -2, 2, -2, 2, -2, 2, -4, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, -4, 4, -4, -4, -4, 4, -4, -4, 4, 4, -4, 4, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389882
    {'cdim': 4, 'counter': 81, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.4a', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, 2, 2, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 13389883
    {'cdim': 4, 'counter': 82, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.4b', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, -2, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -2, 2, 2, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 13389838
    {'cdim': 1, 'counter': 41, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ao', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, -8, 8, -8, 8, 8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, 0, -2, -2, -2, -2, -8, 8, -8, -8, 8, -8, 8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, -2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389839
    {'cdim': 1, 'counter': 42, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ap', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, -8, 8, 8, -8, 8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, 8, -8, 0, -2, -2, -2, -2, -8, 8, -8, -8, 8, -8, 8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, 2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389840
    {'cdim': 1, 'counter': 43, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1aq', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, 8, -8, -8, 8, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 8, 0, 0, 8, 0, 0, 8, 0, 0, -8, -8, 0, -2, -2, -2, -2, -8, 8, -8, 8, -8, -8, 8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, -2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389841
    {'cdim': 1, 'counter': 44, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1ar', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, 8, -8, 8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 8, 0, -2, -2, -2, -2, -8, 8, -8, 8, -8, -8, 8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, 2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389842
    {'cdim': 1, 'counter': 45, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1as', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, -8, -8, 8, -8, 8, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 8, 0, -2, -2, -2, -2, -8, 8, -8, -8, 8, 8, -8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, 2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389843
    {'cdim': 1, 'counter': 46, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1at', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, -8, -8, 8, 8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, 8, 0, 0, 8, 0, 0, -8, -8, 0, -2, -2, -2, -2, -8, 8, -8, -8, 8, 8, -8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, -2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389844
    {'cdim': 1, 'counter': 47, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1au', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, -8, 8, -8, -8, 8, 8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, 0, 8, -8, 0, -2, -2, -2, -2, -8, 8, -8, 8, -8, 8, -8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, -2, -2, -2, 2, 2, 2, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389845
    {'cdim': 1, 'counter': 48, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.1av', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, -8, 8, -8, 8, -8, 8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, 0, -2, -2, -2, -2, -8, 8, -8, 8, -8, 8, -8, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 2, 2, -2, -2, -2, 0, -2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389864
    {'cdim': 2, 'counter': 65, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2q', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, -4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 13389865
    {'cdim': 2, 'counter': 66, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2r', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -8, -8, -8, -8, 0, 0, -4, -8, -8, -8, -8, 8, 8, 8, 8, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, -4, 4, -4, 4, -4, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -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: 13389866
    {'cdim': 2, 'counter': 67, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2s', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -8, -8, -8, -8, 0, 0, -4, 8, 8, 8, 8, 8, -8, -8, 8, -8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, -4, -4, -4, 4, -4, 4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 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: 13389867
    {'cdim': 2, 'counter': 68, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2t', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -8, -8, 8, 8, 0, 0, -4, -8, -8, -8, -8, -8, -8, 8, -8, -8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, 4, 4, -4, -4, -4, 4, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 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: 13389868
    {'cdim': 2, 'counter': 69, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2u', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -8, -8, 8, 8, 0, 0, -4, 8, 8, 8, 8, -8, 8, -8, -8, 8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, -4, -4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, 4, 4, 4, 4, 4, -4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -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: 13389870
    {'cdim': 2, 'counter': 70, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2v', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, -8, -8, 0, 0, -4, -8, -8, -8, -8, -8, 8, -8, -8, 8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, 4, 4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, 4, 4, -4, 4, -4, -4, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 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: 13389871
    {'cdim': 2, 'counter': 71, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2w', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, -8, -8, 0, 0, -4, 8, 8, 8, 8, -8, -8, 8, -8, -8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, 4, 4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, 4, 4, -4, 4, 4, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -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: 13389872
    {'cdim': 2, 'counter': 72, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2x', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, 8, 8, 0, 0, -4, -8, -8, -8, -8, 8, -8, -8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, 4, 4, 4, 4, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, 2, 2, -2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -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: 13389884
    {'cdim': 4, 'counter': 83, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.4c', 'multiplicity': 2, 'nt': [24, 101], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 4, 4, -4, 0, 0, 0, 0, 8, 8, 8, 8, -8, -8, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, 4, 4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 13389873
    {'cdim': 2, 'counter': 73, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2y', 'multiplicity': 8, 'nt': [40, 19], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -16, 0, 16, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -16, -16, 16, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 4, 4, 0, 4, 0, 4, 4, -4, -4, -4, 4, 4, 0, 0, -4, -4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, 4, 4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 13389874
    {'cdim': 2, 'counter': 74, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2z', 'multiplicity': 8, 'nt': [40, 19], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 16, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -16, -16, 16, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -4, -4, 0, -4, 0, -4, -4, 4, 4, 4, -4, -4, 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, 4, 4, 4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 13389875
    {'cdim': 2, 'counter': 75, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2aa', 'multiplicity': 8, 'nt': [40, 19], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, 16, -16, -16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 16, -16, -16, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, -4, -4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13389876
    {'cdim': 2, 'counter': 76, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2ab', 'multiplicity': 8, 'nt': [40, 19], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, 16, 16, 16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 16, -16, -16, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 16, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -4, -4, -4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, -4, -4, -4, 4, 4, -4, 4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13389877
    {'cdim': 2, 'counter': 77, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2ac', 'multiplicity': 8, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, -16, 16, -16, 16, 0, 0, -8, 0, 0, 0, 0, -16, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 8, -8, 8, 8, -8, 8, -8, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, -4, 4, -4, -4, 4, 4, -4, 4, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389878
    {'cdim': 2, 'counter': 78, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2ad', 'multiplicity': 8, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, -16, 16, 16, -16, 0, 0, -8, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 8, -8, 8, -8, 8, 8, -8, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389879
    {'cdim': 2, 'counter': 79, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2ae', 'multiplicity': 8, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 16, -16, -16, 16, 0, 0, -8, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 8, -8, 8, 8, -8, -8, 8, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, -4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}
  • id: 13389881
    {'cdim': 2, 'counter': 80, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.2af', 'multiplicity': 8, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 16, -16, 16, -16, 0, 0, -8, 0, 0, 0, 0, -16, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 8, -8, 8, -8, 8, -8, 8, 4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 4, -4, 4, 4, 4, -4, 4, 4, -4, -4, 4, -4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
  • id: 13389885
    {'cdim': 4, 'counter': 84, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.4d', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, -8, -16, -16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -8, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13389886
    {'cdim': 4, 'counter': 85, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.4e', 'multiplicity': 4, 'nt': [120, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, 0, 0, -8, 16, 16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -8, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -4, 4, 4, -4, 4, -4, 4, -4, 4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13389887
    {'cdim': 4, 'counter': 86, 'faithful': False, 'group': '960.10116', 'group_order': 960, 'image': None, 'label': '960.10116.4f', 'multiplicity': 8, 'nt': [120, 0], 'qdim': 32, 'qvalues': [32, -32, -32, 32, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, 16, 16, -16, 0, 0, 0, 0, -8, -8, -8, -8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 31627943
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  • id: 31628179
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  • id: 31628180
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  • id: 31628181
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  • id: 31628182
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  • id: 31628183
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  • id: 31628184
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  • id: 31628185
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  • id: 31628189
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  • id: 31628192
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  • id: 31628193
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  • id: 31628194
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  • id: 31628195
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  • id: 31628198
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  • id: 31628200
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  • id: 31628201
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  • id: 31628202
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  • id: 31628203
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  • id: 31628204
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  • id: 31628205
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  • id: 31628206
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  • id: 31628207
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  • id: 31628208
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  • id: 31628209
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  • id: 31628211
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  • id: 31628212
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 71, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.d1.a1', 'kernel_order': 96, 'label': '960.10116.1ah3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[1, -2]], [[1, 2]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[1, -2]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -2]], [[-1, -2]], [[1, 2]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[-1, -1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[-1, -1]], [[1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[-1, 2]], [[-1, -2]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[-1, -1]], [[1, 2]], [[-1, -2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[1, -1]], [[-1, -2]], [[-1, -2]], [[1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, 2]], [[-1, 2]], [[1, 1]]]}
  • id: 31628213
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 72, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.d1.a1', 'kernel_order': 96, 'label': '960.10116.1ah4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, -2]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[1, 2]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 2]], [[-1, 2]], [[1, -2]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[-1, 2]], [[-1, -2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[-1, 1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[-1, 1]], [[1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[-1, -2]], [[-1, 2]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[-1, 1]], [[1, -2]], [[-1, 2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[1, 1]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[-1, -2]], [[-1, -2]], [[1, -1]]]}
  • id: 31628214
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  • id: 31628215
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  • id: 31628216
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  • id: 31628217
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  • id: 31628218
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  • id: 31628219
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  • id: 31628220
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  • id: 31628222
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  • id: 31628223
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  • id: 31628224
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  • id: 31628225
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  • id: 31628226
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  • id: 31628227
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  • id: 31628228
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  • id: 31628229
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  • id: 31628230
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  • id: 31628231
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  • id: 31628233
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  • id: 31628234
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  • id: 31628235
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  • id: 31628236
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  • id: 31628237
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  • id: 31628238
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  • id: 31628239
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  • id: 31628240
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  • id: 31628241
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 98, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.h1', 'kernel_order': 48, 'label': '960.10116.1ao2', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 4]], [[1, 8]], [[1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[1, 6]], [[1, 4]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[1, 6]], [[1, 8]], [[-1, 6]], [[1, 4]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[-1, 7]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 9]], [[-1, 9]], [[-1, 7]], [[1, 7]], [[1, 7]], [[-1, 3]], [[1, 9]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 9]], [[1, 1]], [[1, 4]], [[-1, 1]], [[-1, 3]], [[-1, 8]], [[-1, 7]], [[1, 1]], [[-1, 1]], [[1, 9]], [[-1, 2]], [[-1, 9]], [[1, 9]], [[-1, 9]], [[-1, 1]], [[1, 3]], [[1, 6]], [[-1, 9]], [[-1, 7]], [[1, 7]], [[-1, 6]], [[1, 3]], [[-1, 3]], [[1, 2]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 4]], [[1, 7]], [[1, 7]], [[1, 9]], [[1, 1]], [[-1, 7]], [[1, 8]], [[1, 6]], [[1, 6]], [[1, 2]], [[-1, 6]], [[1, 8]], [[1, 7]], [[1, 9]], [[1, 2]], [[1, 3]], [[-1, 1]], [[1, 4]], [[-1, 3]], [[-1, 6]], [[-1, 7]], [[1, 9]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 9]], [[1, 1]], [[-1, 8]], [[-1, 4]], [[-1, 9]], [[-1, 1]], [[-1, 2]], [[-1, 7]], [[1, 7]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[1, 8]], [[1, 7]], [[1, 8]], [[1, 2]], [[1, 3]], [[-1, 1]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 7]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[1, 9]], [[1, 3]], [[-1, 1]], [[-1, 9]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 4]], [[1, 1]], [[1, 9]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[1, 1]], [[-1, 7]], [[-1, 8]], [[1, 6]], [[1, 9]], [[-1, 3]], [[1, 7]], [[1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[1, 8]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[1, 8]], [[1, 4]], [[1, 6]], [[1, 6]], [[1, 8]], [[-1, 6]], [[-1, 4]], [[-1, 4]], [[-1, 8]], [[-1, 9]], [[-1, 7]], [[-1, 3]], [[1, 7]], [[1, 9]], [[-1, 9]], [[1, 3]], [[-1, 1]], [[-1, 7]], [[1, 1]], [[1, 9]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 7]], [[1, 2]], [[-1, 7]], [[-1, 7]], [[1, 9]], [[1, 7]], [[-1, 1]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 6]], [[-1, 1]], [[-1, 9]], [[1, 4]], [[-1, 3]], [[-1, 6]], [[1, 1]], [[1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 8]], [[1, 8]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[1, 9]], [[-1, 4]], [[1, 7]]]}
  • id: 31628242
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 99, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.h1', 'kernel_order': 48, 'label': '960.10116.1ao3', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 4]], [[1, 8]], [[1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[1, 6]], [[1, 4]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[1, 6]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 9]], [[1, 9]], [[1, 7]], [[-1, 7]], [[-1, 7]], [[1, 3]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 1]], [[1, 4]], [[1, 1]], [[1, 3]], [[-1, 8]], [[1, 7]], [[-1, 1]], [[1, 1]], [[-1, 9]], [[-1, 2]], [[1, 9]], [[-1, 9]], [[1, 9]], [[1, 1]], [[-1, 3]], [[1, 6]], [[1, 9]], [[1, 7]], [[-1, 7]], [[-1, 6]], [[-1, 3]], [[1, 3]], [[1, 2]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 4]], [[-1, 7]], [[-1, 7]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[1, 8]], [[1, 6]], [[1, 6]], [[1, 2]], [[-1, 6]], [[1, 8]], [[-1, 7]], [[-1, 9]], [[1, 2]], [[-1, 3]], [[1, 1]], [[1, 4]], [[1, 3]], [[-1, 6]], [[1, 7]], [[-1, 9]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 9]], [[-1, 1]], [[-1, 8]], [[-1, 4]], [[1, 9]], [[1, 1]], [[-1, 2]], [[1, 7]], [[-1, 7]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[1, 8]], [[-1, 7]], [[1, 8]], [[1, 2]], [[-1, 3]], [[1, 1]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[1, 7]], [[1, 1]], [[1, 9]], [[-1, 3]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[1, 9]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 4]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[1, 7]], [[-1, 8]], [[1, 6]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[1, 8]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[1, 8]], [[1, 4]], [[1, 6]], [[1, 6]], [[1, 8]], [[-1, 6]], [[-1, 4]], [[-1, 4]], [[-1, 8]], [[1, 9]], [[1, 7]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 1]], [[1, 7]], [[-1, 1]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 7]], [[1, 2]], [[1, 7]], [[1, 7]], [[-1, 9]], [[-1, 7]], [[1, 1]], [[1, 9]], [[-1, 1]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 6]], [[1, 1]], [[1, 9]], [[1, 4]], [[1, 3]], [[-1, 6]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[1, 3]], [[-1, 8]], [[1, 8]], [[1, 9]], [[-1, 3]], [[1, 3]], [[-1, 9]], [[1, 7]], [[-1, 9]], [[-1, 4]], [[-1, 7]]]}
  • id: 31627945
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  • id: 31627946
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  • id: 31627947
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  • id: 31627948
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  • id: 31627949
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  • id: 31627950
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  • id: 31627951
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  • id: 31627952
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  • id: 31627953
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  • id: 31627954
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  • id: 31627956
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  • id: 31627957
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  • id: 31627958
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  • id: 31627959
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 113, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.f1', 'kernel_order': 48, 'label': '960.10116.1aq1', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 4]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 8]], [[1, 6]], [[-1, 2]], [[-1, 8]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[1, 6]], [[1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 9]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 7]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[-1, 9]], [[1, 6]], [[-1, 9]], [[-1, 7]], [[-1, 2]], [[-1, 3]], [[1, 9]], [[1, 9]], [[1, 1]], [[-1, 8]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 9]], [[1, 7]], [[1, 4]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 4]], [[-1, 7]], [[1, 7]], [[1, 8]], [[1, 7]], [[-1, 7]], [[-1, 9]], [[-1, 6]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 9]], [[-1, 3]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, 8]], [[-1, 4]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, 8]], [[1, 7]], [[-1, 9]], [[1, 6]], [[-1, 7]], [[-1, 4]], [[-1, 3]], [[1, 1]], [[1, 7]], [[1, 9]], [[-1, 7]], [[-1, 1]], [[1, 9]], [[-1, 2]], [[-1, 6]], [[-1, 1]], [[-1, 9]], [[-1, 8]], [[-1, 3]], [[1, 3]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[-1, 6]], [[-1, 2]], [[1, 3]], [[1, 2]], [[1, 8]], [[-1, 7]], [[1, 9]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 3]], [[1, 9]], [[1, 1]], [[-1, 7]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 1]], [[1, 7]], [[-1, 9]], [[-1, 1]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[-1, 6]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[1, 3]], [[-1, 2]], [[1, 4]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[-1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 6]], [[-1, 6]], [[1, 2]], [[1, 1]], [[1, 3]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[1, 9]], [[1, 3]], [[-1, 9]], [[-1, 1]], [[-1, 7]], [[1, 9]], [[-1, 9]], [[1, 7]], [[-1, 3]], [[1, 8]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 9]], [[-1, 1]], [[1, 9]], [[1, 3]], [[-1, 9]], [[1, 7]], [[-1, 7]], [[1, 4]], [[1, 9]], [[1, 1]], [[1, 6]], [[-1, 7]], [[-1, 4]], [[-1, 9]], [[1, 9]], [[-1, 8]], [[1, 7]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 6]], [[1, 3]]]}
  • id: 31627960
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  • id: 31627961
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  • id: 31627962
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 116, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.f1', 'kernel_order': 48, 'label': '960.10116.1aq4', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[1, 5]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 4]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 8]], [[1, 6]], [[-1, 2]], [[-1, 8]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[1, 6]], [[1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 7]], [[1, 9]], [[-1, 9]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 7]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 1]], [[1, 9]], [[1, 6]], [[1, 9]], [[1, 7]], [[-1, 2]], [[1, 3]], [[-1, 9]], [[-1, 9]], [[-1, 1]], [[-1, 8]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 9]], [[-1, 7]], [[1, 4]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 4]], [[1, 7]], [[-1, 7]], [[1, 8]], [[-1, 7]], [[1, 7]], [[1, 9]], [[-1, 6]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, 8]], [[-1, 4]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 8]], [[-1, 7]], [[1, 9]], [[1, 6]], [[1, 7]], [[-1, 4]], [[1, 3]], [[-1, 1]], [[-1, 7]], [[-1, 9]], [[1, 7]], [[1, 1]], [[-1, 9]], [[-1, 2]], [[-1, 6]], [[1, 1]], [[1, 9]], [[-1, 8]], [[1, 3]], [[-1, 3]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[-1, 6]], [[-1, 2]], [[-1, 3]], [[1, 2]], [[1, 8]], [[1, 7]], [[-1, 9]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 3]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 1]], [[-1, 7]], [[1, 9]], [[1, 1]], [[1, 3]], [[-1, 9]], [[1, 7]], [[-1, 6]], [[1, 9]], [[1, 1]], [[-1, 7]], [[1, 3]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[-1, 2]], [[1, 4]], [[1, 1]], [[-1, 7]], [[1, 3]], [[-1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 6]], [[-1, 6]], [[1, 2]], [[-1, 1]], [[-1, 3]], [[-1, 7]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[-1, 3]], [[1, 9]], [[1, 1]], [[1, 7]], [[-1, 9]], [[1, 9]], [[-1, 7]], [[1, 3]], [[1, 8]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 9]], [[1, 1]], [[-1, 9]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[1, 7]], [[1, 4]], [[-1, 9]], [[-1, 1]], [[1, 6]], [[1, 7]], [[-1, 4]], [[1, 9]], [[-1, 9]], [[-1, 8]], [[-1, 7]], [[-1, 2]], [[1, 2]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 6]], [[-1, 3]]]}
  • id: 31627963
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 117, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.f1', 'kernel_order': 48, 'label': '960.10116.1aq5', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 8]], [[1, 6]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 6]], [[1, 4]], [[-1, 8]], [[-1, 6]], [[-1, 4]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 8]], [[1, 4]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[-1, 8]], [[1, 4]], [[1, 6]], [[-1, 4]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 8]], [[1, 4]], [[-1, 6]], [[-1, 2]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 7]], [[-1, 3]], [[-1, 3]], [[-1, 9]], [[1, 9]], [[1, 9]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[1, 3]], [[1, 7]], [[-1, 8]], [[1, 7]], [[1, 1]], [[-1, 6]], [[1, 9]], [[-1, 7]], [[-1, 7]], [[-1, 3]], [[-1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 7]], [[-1, 1]], [[-1, 2]], [[1, 3]], [[-1, 9]], [[1, 9]], [[1, 2]], [[1, 1]], [[-1, 1]], [[1, 4]], [[-1, 1]], [[1, 1]], [[1, 7]], [[1, 8]], [[-1, 9]], [[-1, 9]], [[-1, 3]], [[-1, 7]], [[1, 9]], [[1, 6]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 2]], [[1, 6]], [[-1, 9]], [[-1, 3]], [[1, 4]], [[-1, 1]], [[1, 7]], [[-1, 8]], [[1, 1]], [[1, 2]], [[1, 9]], [[-1, 3]], [[-1, 1]], [[-1, 7]], [[1, 1]], [[1, 3]], [[-1, 7]], [[-1, 6]], [[1, 8]], [[1, 3]], [[1, 7]], [[-1, 4]], [[1, 9]], [[-1, 9]], [[-1, 8]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[1, 8]], [[-1, 6]], [[-1, 9]], [[1, 6]], [[1, 4]], [[1, 1]], [[-1, 7]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 9]], [[-1, 7]], [[-1, 3]], [[1, 1]], [[-1, 2]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 3]], [[-1, 1]], [[1, 7]], [[1, 3]], [[1, 9]], [[-1, 7]], [[1, 1]], [[1, 8]], [[1, 7]], [[1, 3]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[-1, 6]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 9]], [[1, 8]], [[1, 4]], [[1, 6]], [[-1, 4]], [[-1, 6]], [[-1, 8]], [[1, 4]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 8]], [[1, 2]], [[1, 4]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[-1, 8]], [[-1, 4]], [[1, 6]], [[1, 8]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[-1, 8]], [[1, 8]], [[1, 6]], [[-1, 3]], [[-1, 9]], [[-1, 1]], [[1, 9]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[-1, 9]], [[1, 7]], [[1, 3]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[1, 9]], [[1, 4]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 9]], [[1, 7]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[1, 1]], [[-1, 2]], [[-1, 7]], [[-1, 3]], [[-1, 8]], [[1, 1]], [[1, 2]], [[1, 7]], [[-1, 7]], [[-1, 4]], [[-1, 1]], [[-1, 6]], [[1, 6]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 9]], [[1, 3]], [[1, 8]], [[-1, 9]]]}
  • id: 31627964
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  • id: 31627965
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  • id: 31627967
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  • id: 31627968
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  • id: 31627969
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  • id: 31627970
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 123, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.e1', 'kernel_order': 48, 'label': '960.10116.1ar3', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 0]], [[1, 5]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[1, 8]], [[-1, 2]], [[-1, 4]], [[1, 8]], [[1, 2]], [[-1, 6]], [[-1, 8]], [[1, 4]], [[-1, 6]], [[1, 6]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 4]], [[1, 2]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 9]], [[1, 9]], [[1, 7]], [[-1, 7]], [[-1, 7]], [[1, 3]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[-1, 3]], [[1, 8]], [[-1, 7]], [[1, 1]], [[1, 1]], [[1, 9]], [[1, 2]], [[1, 9]], [[-1, 9]], [[-1, 9]], [[-1, 1]], [[1, 3]], [[-1, 6]], [[-1, 9]], [[1, 7]], [[-1, 7]], [[1, 6]], [[-1, 3]], [[1, 3]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 4]], [[1, 7]], [[1, 7]], [[1, 9]], [[1, 1]], [[-1, 7]], [[-1, 8]], [[1, 6]], [[1, 6]], [[1, 2]], [[-1, 6]], [[1, 8]], [[-1, 7]], [[-1, 9]], [[1, 2]], [[-1, 3]], [[1, 1]], [[1, 4]], [[1, 3]], [[-1, 6]], [[1, 7]], [[-1, 9]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 9]], [[-1, 1]], [[-1, 8]], [[-1, 4]], [[1, 9]], [[1, 1]], [[-1, 2]], [[1, 7]], [[-1, 7]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 7]], [[1, 8]], [[1, 2]], [[1, 3]], [[-1, 1]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 7]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[1, 6]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[1, 9]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 4]], [[1, 1]], [[1, 9]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[1, 1]], [[-1, 7]], [[-1, 8]], [[1, 6]], [[1, 9]], [[-1, 3]], [[1, 7]], [[-1, 4]], [[1, 2]], [[-1, 8]], [[1, 2]], [[1, 8]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 6]], [[-1, 2]], [[1, 8]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 8]], [[1, 4]], [[-1, 6]], [[1, 6]], [[1, 8]], [[-1, 6]], [[-1, 4]], [[1, 4]], [[-1, 8]], [[1, 9]], [[1, 7]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 1]], [[1, 7]], [[-1, 1]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 7]], [[-1, 2]], [[1, 7]], [[-1, 7]], [[1, 9]], [[-1, 7]], [[-1, 1]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 6]], [[1, 1]], [[1, 9]], [[-1, 4]], [[-1, 3]], [[1, 6]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 8]], [[-1, 8]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[-1, 9]], [[1, 4]], [[1, 7]]]}
  • id: 31627971
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  • id: 31627972
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  • id: 31627973
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  • id: 31627974
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  • id: 31627975
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  • id: 31627976
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  • id: 31627978
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  • id: 31627979
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 131, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.d1', 'kernel_order': 48, 'label': '960.10116.1as3', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 0]], [[1, 5]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 8]], [[1, 2]], [[1, 4]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 6]], [[-1, 4]], [[1, 2]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[1, 6]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 9]], [[1, 9]], [[1, 7]], [[-1, 7]], [[-1, 7]], [[1, 3]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[1, 3]], [[1, 8]], [[1, 7]], [[-1, 1]], [[-1, 1]], [[-1, 9]], [[1, 2]], [[-1, 9]], [[1, 9]], [[1, 9]], [[1, 1]], [[-1, 3]], [[-1, 6]], [[-1, 9]], [[-1, 7]], [[1, 7]], [[1, 6]], [[1, 3]], [[-1, 3]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 4]], [[-1, 7]], [[1, 7]], [[1, 9]], [[1, 1]], [[-1, 7]], [[-1, 8]], [[-1, 6]], [[-1, 6]], [[-1, 2]], [[1, 6]], [[-1, 8]], [[1, 7]], [[1, 9]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[-1, 4]], [[-1, 3]], [[1, 6]], [[-1, 7]], [[1, 9]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 9]], [[1, 1]], [[1, 8]], [[1, 4]], [[-1, 9]], [[-1, 1]], [[1, 2]], [[-1, 7]], [[1, 7]], [[-1, 4]], [[1, 2]], [[-1, 8]], [[1, 8]], [[1, 4]], [[-1, 8]], [[-1, 7]], [[1, 8]], [[1, 2]], [[-1, 3]], [[1, 1]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 7]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[1, 6]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[1, 9]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 4]], [[1, 1]], [[1, 9]], [[-1, 3]], [[1, 7]], [[1, 9]], [[-1, 1]], [[1, 7]], [[-1, 8]], [[1, 6]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[-1, 4]], [[1, 2]], [[-1, 8]], [[1, 2]], [[1, 8]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[-1, 4]], [[1, 8]], [[1, 9]], [[1, 7]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 1]], [[1, 7]], [[-1, 1]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 7]], [[-1, 2]], [[-1, 7]], [[-1, 7]], [[1, 9]], [[1, 7]], [[1, 1]], [[1, 9]], [[-1, 1]], [[1, 7]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 6]], [[-1, 1]], [[-1, 9]], [[-1, 4]], [[-1, 3]], [[1, 6]], [[1, 1]], [[1, 1]], [[1, 2]], [[-1, 3]], [[1, 8]], [[-1, 8]], [[-1, 9]], [[1, 3]], [[1, 3]], [[-1, 9]], [[1, 7]], [[1, 9]], [[1, 4]], [[-1, 7]]]}
  • id: 31627980
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 132, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.d1', 'kernel_order': 48, 'label': '960.10116.1as4', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[1, 0]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 4]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 8]], [[1, 2]], [[-1, 8]], [[-1, 6]], [[1, 2]], [[1, 8]], [[-1, 4]], [[-1, 2]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 4]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 7]], [[1, 9]], [[-1, 9]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 7]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 1]], [[1, 9]], [[1, 6]], [[1, 9]], [[-1, 7]], [[-1, 2]], [[-1, 3]], [[1, 9]], [[1, 9]], [[1, 1]], [[-1, 8]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 9]], [[1, 7]], [[1, 4]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 4]], [[-1, 7]], [[1, 7]], [[1, 8]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[-1, 6]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, 8]], [[-1, 4]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 8]], [[-1, 7]], [[1, 9]], [[1, 6]], [[1, 7]], [[-1, 4]], [[1, 3]], [[-1, 1]], [[-1, 7]], [[-1, 9]], [[1, 7]], [[1, 1]], [[-1, 9]], [[-1, 2]], [[-1, 6]], [[1, 1]], [[1, 9]], [[-1, 8]], [[1, 3]], [[-1, 3]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[-1, 6]], [[1, 2]], [[1, 3]], [[-1, 2]], [[-1, 8]], [[1, 7]], [[-1, 9]], [[1, 4]], [[1, 8]], [[-1, 6]], [[1, 3]], [[1, 9]], [[1, 1]], [[-1, 7]], [[-1, 4]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 1]], [[1, 7]], [[-1, 9]], [[-1, 1]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[1, 6]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[1, 2]], [[-1, 4]], [[1, 1]], [[-1, 7]], [[1, 3]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 8]], [[1, 8]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[1, 6]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[-1, 7]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[-1, 3]], [[1, 9]], [[1, 1]], [[1, 7]], [[-1, 9]], [[1, 9]], [[-1, 7]], [[1, 3]], [[1, 8]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 9]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[1, 9]], [[1, 7]], [[-1, 7]], [[1, 4]], [[1, 9]], [[1, 1]], [[1, 6]], [[1, 7]], [[-1, 4]], [[-1, 9]], [[-1, 9]], [[-1, 8]], [[1, 7]], [[-1, 2]], [[1, 2]], [[1, 1]], [[-1, 7]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 6]], [[1, 3]]]}
  • id: 31627981
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  • id: 31627982
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  • id: 31627983
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  • id: 31627984
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  • id: 31627985
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  • id: 31627986
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  • id: 31627987
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  • id: 31627989
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  • id: 31627990
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  • id: 31627991
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  • id: 31627992
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  • id: 31627993
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  • id: 31627994
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  • id: 31627995
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  • id: 31627996
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  • id: 31627997
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  • id: 31627998
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 149, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.b1', 'kernel_order': 48, 'label': '960.10116.1au5', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 6]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 6]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 2]], [[1, 6]], [[1, 8]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 8]], [[1, 4]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[-1, 8]], [[1, 4]], [[1, 6]], [[-1, 4]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 8]], [[1, 4]], [[-1, 6]], [[-1, 2]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 7]], [[-1, 3]], [[-1, 3]], [[-1, 9]], [[1, 9]], [[1, 9]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[1, 3]], [[1, 7]], [[1, 8]], [[-1, 7]], [[1, 1]], [[1, 6]], [[1, 9]], [[-1, 7]], [[1, 7]], [[-1, 3]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 7]], [[-1, 1]], [[1, 2]], [[-1, 3]], [[1, 9]], [[-1, 9]], [[-1, 2]], [[-1, 1]], [[1, 1]], [[-1, 4]], [[1, 1]], [[-1, 1]], [[-1, 7]], [[-1, 8]], [[-1, 9]], [[1, 9]], [[1, 3]], [[1, 7]], [[-1, 9]], [[-1, 6]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 6]], [[1, 9]], [[1, 3]], [[-1, 4]], [[1, 1]], [[-1, 7]], [[1, 8]], [[-1, 1]], [[-1, 2]], [[-1, 9]], [[1, 3]], [[1, 1]], [[1, 7]], [[-1, 1]], [[-1, 3]], [[1, 7]], [[1, 6]], [[-1, 8]], [[-1, 3]], [[-1, 7]], [[1, 4]], [[-1, 9]], [[1, 9]], [[1, 8]], [[1, 4]], [[-1, 6]], [[1, 6]], [[-1, 8]], [[1, 6]], [[-1, 9]], [[1, 6]], [[1, 4]], [[1, 1]], [[-1, 7]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[1, 9]], [[1, 7]], [[1, 3]], [[-1, 1]], [[1, 2]], [[1, 4]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[-1, 3]], [[-1, 1]], [[1, 7]], [[1, 3]], [[1, 9]], [[-1, 7]], [[1, 1]], [[1, 8]], [[-1, 7]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[-1, 6]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 9]], [[-1, 8]], [[-1, 4]], [[1, 6]], [[-1, 4]], [[-1, 6]], [[-1, 8]], [[1, 4]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 8]], [[1, 2]], [[1, 4]], [[-1, 6]], [[-1, 4]], [[-1, 4]], [[-1, 8]], [[1, 4]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 8]], [[1, 8]], [[-1, 6]], [[-1, 3]], [[-1, 9]], [[-1, 1]], [[1, 9]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[-1, 9]], [[1, 7]], [[1, 3]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[1, 9]], [[-1, 4]], [[1, 9]], [[-1, 9]], [[1, 3]], [[-1, 9]], [[1, 7]], [[1, 3]], [[-1, 7]], [[1, 9]], [[-1, 7]], [[-1, 1]], [[-1, 1]], [[1, 2]], [[1, 7]], [[1, 3]], [[1, 8]], [[-1, 1]], [[-1, 2]], [[-1, 7]], [[1, 7]], [[1, 4]], [[1, 1]], [[1, 6]], [[-1, 6]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[1, 9]], [[-1, 3]], [[-1, 8]], [[-1, 9]]]}
  • id: 31628000
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 150, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.b1', 'kernel_order': 48, 'label': '960.10116.1au6', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 4]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 4]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 8]], [[-1, 4]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 8]], [[1, 2]], [[-1, 6]], [[1, 4]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 6]], [[-1, 4]], [[1, 6]], [[-1, 8]], [[1, 4]], [[1, 8]], [[-1, 2]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 8]], [[1, 1]], [[-1, 9]], [[-1, 3]], [[1, 3]], [[1, 7]], [[1, 7]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 9]], [[-1, 7]], [[1, 9]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[-1, 3]], [[-1, 2]], [[1, 3]], [[-1, 9]], [[-1, 4]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 7]], [[-1, 6]], [[-1, 7]], [[1, 7]], [[-1, 7]], [[-1, 3]], [[1, 9]], [[-1, 8]], [[1, 7]], [[-1, 1]], [[1, 1]], [[1, 8]], [[1, 9]], [[-1, 9]], [[1, 6]], [[-1, 9]], [[1, 9]], [[1, 3]], [[1, 2]], [[1, 1]], [[-1, 1]], [[-1, 7]], [[-1, 3]], [[1, 1]], [[1, 4]], [[-1, 8]], [[-1, 8]], [[1, 6]], [[1, 8]], [[1, 4]], [[-1, 1]], [[-1, 7]], [[1, 6]], [[-1, 9]], [[1, 3]], [[-1, 2]], [[1, 9]], [[1, 8]], [[1, 1]], [[-1, 7]], [[-1, 9]], [[-1, 3]], [[1, 9]], [[1, 7]], [[-1, 3]], [[-1, 4]], [[1, 2]], [[1, 7]], [[1, 3]], [[-1, 6]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 1]], [[-1, 4]], [[-1, 6]], [[-1, 9]], [[1, 3]], [[-1, 8]], [[1, 6]], [[1, 2]], [[-1, 1]], [[-1, 3]], [[-1, 7]], [[1, 9]], [[-1, 8]], [[-1, 6]], [[1, 4]], [[1, 8]], [[-1, 2]], [[1, 7]], [[1, 9]], [[-1, 3]], [[-1, 7]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[-1, 2]], [[1, 3]], [[1, 7]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 3]], [[1, 1]], [[1, 4]], [[1, 8]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[1, 2]], [[1, 6]], [[-1, 4]], [[1, 6]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 6]], [[1, 2]], [[-1, 8]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[1, 4]], [[1, 6]], [[1, 6]], [[1, 2]], [[-1, 6]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 7]], [[1, 1]], [[1, 9]], [[-1, 1]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 7]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 9]], [[-1, 1]], [[1, 6]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 7]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 9]], [[1, 9]], [[-1, 8]], [[-1, 3]], [[-1, 7]], [[-1, 2]], [[1, 9]], [[1, 8]], [[1, 3]], [[-1, 3]], [[-1, 6]], [[-1, 9]], [[-1, 4]], [[1, 4]], [[1, 7]], [[-1, 9]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[1, 7]], [[1, 2]], [[1, 1]]]}
  • id: 31628001
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  • id: 31628002
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 152, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.b1', 'kernel_order': 48, 'label': '960.10116.1au8', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 8]], [[1, 6]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 6]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 2]], [[1, 6]], [[1, 8]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 8]], [[1, 4]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[-1, 8]], [[1, 4]], [[1, 6]], [[-1, 4]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 8]], [[1, 4]], [[-1, 6]], [[-1, 2]], [[1, 9]], [[-1, 1]], [[-1, 7]], [[1, 7]], [[1, 3]], [[1, 3]], [[1, 9]], [[-1, 9]], [[-1, 9]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[-1, 7]], [[1, 8]], [[1, 7]], [[-1, 1]], [[1, 6]], [[-1, 9]], [[1, 7]], [[-1, 7]], [[1, 3]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 7]], [[1, 1]], [[1, 2]], [[1, 3]], [[-1, 9]], [[1, 9]], [[-1, 2]], [[1, 1]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[1, 1]], [[1, 7]], [[-1, 8]], [[1, 9]], [[-1, 9]], [[-1, 3]], [[-1, 7]], [[1, 9]], [[-1, 6]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 6]], [[-1, 9]], [[-1, 3]], [[-1, 4]], [[-1, 1]], [[1, 7]], [[1, 8]], [[1, 1]], [[-1, 2]], [[1, 9]], [[-1, 3]], [[-1, 1]], [[-1, 7]], [[1, 1]], [[1, 3]], [[-1, 7]], [[1, 6]], [[-1, 8]], [[1, 3]], [[1, 7]], [[1, 4]], [[1, 9]], [[-1, 9]], [[1, 8]], [[1, 4]], [[-1, 6]], [[1, 6]], [[-1, 8]], [[1, 6]], [[1, 9]], [[1, 6]], [[1, 4]], [[-1, 1]], [[1, 7]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 9]], [[-1, 7]], [[-1, 3]], [[1, 1]], [[1, 2]], [[1, 4]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[1, 3]], [[1, 1]], [[-1, 7]], [[-1, 3]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[1, 8]], [[1, 7]], [[1, 3]], [[-1, 1]], [[1, 9]], [[1, 3]], [[-1, 7]], [[1, 9]], [[-1, 6]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 8]], [[-1, 4]], [[1, 6]], [[-1, 4]], [[-1, 6]], [[-1, 8]], [[1, 4]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 8]], [[1, 2]], [[1, 4]], [[-1, 6]], [[-1, 4]], [[-1, 4]], [[-1, 8]], [[1, 4]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 8]], [[1, 8]], [[-1, 6]], [[1, 3]], [[1, 9]], [[1, 1]], [[-1, 9]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 7]], [[1, 9]], [[-1, 7]], [[-1, 3]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 1]], [[-1, 9]], [[-1, 4]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[1, 7]], [[1, 1]], [[1, 1]], [[1, 2]], [[-1, 7]], [[-1, 3]], [[1, 8]], [[1, 1]], [[-1, 2]], [[1, 7]], [[-1, 7]], [[1, 4]], [[-1, 1]], [[1, 6]], [[-1, 6]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[1, 3]], [[-1, 8]], [[1, 9]]]}
  • id: 31628003
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 153, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.a1', 'kernel_order': 48, 'label': '960.10116.1av1', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 4]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 8]], [[-1, 4]], [[1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[1, 4]], [[1, 6]], [[1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[-1, 6]], [[-1, 8]], [[-1, 2]], [[1, 8]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 9]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 7]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[-1, 9]], [[-1, 6]], [[1, 9]], [[-1, 7]], [[1, 2]], [[-1, 3]], [[1, 9]], [[-1, 9]], [[1, 1]], [[1, 8]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 9]], [[1, 7]], [[-1, 4]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 4]], [[1, 7]], [[-1, 7]], [[-1, 8]], [[-1, 7]], [[1, 7]], [[1, 9]], [[1, 6]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 8]], [[-1, 4]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, 8]], [[1, 7]], [[-1, 9]], [[1, 6]], [[-1, 7]], [[-1, 4]], [[-1, 3]], [[1, 1]], [[1, 7]], [[1, 9]], [[-1, 7]], [[-1, 1]], [[1, 9]], [[-1, 2]], [[-1, 6]], [[-1, 1]], [[-1, 9]], [[-1, 8]], [[-1, 3]], [[1, 3]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[-1, 6]], [[-1, 2]], [[-1, 3]], [[-1, 2]], [[-1, 8]], [[1, 7]], [[-1, 9]], [[1, 4]], [[1, 8]], [[-1, 6]], [[1, 3]], [[1, 9]], [[1, 1]], [[-1, 7]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 1]], [[-1, 7]], [[1, 9]], [[1, 1]], [[1, 3]], [[-1, 9]], [[1, 7]], [[1, 6]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[1, 2]], [[-1, 4]], [[1, 1]], [[-1, 7]], [[1, 3]], [[-1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 8]], [[1, 6]], [[1, 8]], [[1, 2]], [[1, 6]], [[1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 6]], [[-1, 2]], [[1, 1]], [[1, 3]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[1, 9]], [[1, 3]], [[-1, 9]], [[-1, 1]], [[-1, 7]], [[1, 9]], [[-1, 9]], [[1, 7]], [[-1, 3]], [[-1, 8]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[1, 9]], [[1, 7]], [[1, 7]], [[-1, 4]], [[-1, 9]], [[-1, 1]], [[-1, 6]], [[1, 7]], [[1, 4]], [[1, 9]], [[-1, 9]], [[1, 8]], [[-1, 7]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, 7]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 6]], [[1, 3]]]}
  • id: 31628004
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  • id: 31628005
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 155, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.a1', 'kernel_order': 48, 'label': '960.10116.1av3', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[1, 8]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[-1, 8]], [[1, 4]], [[-1, 6]], [[1, 6]], [[-1, 6]], [[-1, 4]], [[-1, 2]], [[1, 8]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 6]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 9]], [[1, 9]], [[1, 7]], [[-1, 7]], [[-1, 7]], [[1, 3]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 1]], [[1, 4]], [[1, 1]], [[-1, 3]], [[-1, 8]], [[-1, 7]], [[1, 1]], [[-1, 1]], [[1, 9]], [[-1, 2]], [[-1, 9]], [[1, 9]], [[-1, 9]], [[-1, 1]], [[1, 3]], [[1, 6]], [[1, 9]], [[-1, 7]], [[1, 7]], [[-1, 6]], [[1, 3]], [[-1, 3]], [[1, 2]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 4]], [[1, 7]], [[-1, 7]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[1, 8]], [[-1, 6]], [[-1, 6]], [[-1, 2]], [[1, 6]], [[-1, 8]], [[1, 7]], [[1, 9]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[-1, 4]], [[-1, 3]], [[1, 6]], [[-1, 7]], [[1, 9]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 9]], [[1, 1]], [[1, 8]], [[1, 4]], [[-1, 9]], [[-1, 1]], [[1, 2]], [[-1, 7]], [[1, 7]], [[-1, 4]], [[1, 2]], [[-1, 8]], [[1, 8]], [[1, 4]], [[1, 8]], [[-1, 7]], [[1, 8]], [[1, 2]], [[1, 3]], [[-1, 1]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[1, 7]], [[1, 1]], [[1, 9]], [[-1, 3]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[1, 9]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 4]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 1]], [[-1, 7]], [[-1, 8]], [[1, 6]], [[1, 9]], [[-1, 3]], [[1, 7]], [[1, 4]], [[-1, 2]], [[-1, 8]], [[1, 2]], [[1, 8]], [[-1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 6]], [[-1, 2]], [[1, 8]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 4]], [[1, 8]], [[1, 9]], [[1, 7]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 1]], [[1, 7]], [[-1, 1]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 7]], [[1, 2]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[-1, 9]], [[1, 1]], [[-1, 7]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 6]], [[-1, 1]], [[-1, 9]], [[1, 4]], [[1, 3]], [[-1, 6]], [[1, 1]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 8]], [[1, 8]], [[1, 9]], [[-1, 3]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[1, 9]], [[-1, 4]], [[1, 7]]]}
  • id: 31628006
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 156, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.a1', 'kernel_order': 48, 'label': '960.10116.1av4', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 4]], [[-1, 2]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[-1, 8]], [[1, 6]], [[1, 2]], [[1, 8]], [[-1, 4]], [[1, 2]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[1, 4]], [[1, 6]], [[1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[-1, 6]], [[-1, 8]], [[-1, 2]], [[1, 8]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 7]], [[1, 9]], [[-1, 9]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 7]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 1]], [[1, 9]], [[-1, 6]], [[-1, 9]], [[1, 7]], [[1, 2]], [[1, 3]], [[-1, 9]], [[1, 9]], [[-1, 1]], [[1, 8]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 9]], [[-1, 7]], [[-1, 4]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 4]], [[-1, 7]], [[1, 7]], [[-1, 8]], [[1, 7]], [[-1, 7]], [[-1, 9]], [[1, 6]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 9]], [[-1, 3]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 8]], [[-1, 4]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 8]], [[-1, 7]], [[1, 9]], [[1, 6]], [[1, 7]], [[-1, 4]], [[1, 3]], [[-1, 1]], [[-1, 7]], [[-1, 9]], [[1, 7]], [[1, 1]], [[-1, 9]], [[-1, 2]], [[-1, 6]], [[1, 1]], [[1, 9]], [[-1, 8]], [[1, 3]], [[-1, 3]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 2]], [[-1, 6]], [[-1, 2]], [[1, 3]], [[-1, 2]], [[-1, 8]], [[-1, 7]], [[1, 9]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 3]], [[-1, 9]], [[-1, 1]], [[1, 7]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 1]], [[1, 7]], [[-1, 9]], [[-1, 1]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[1, 6]], [[1, 9]], [[1, 1]], [[-1, 7]], [[1, 3]], [[1, 1]], [[-1, 9]], [[1, 3]], [[1, 2]], [[-1, 4]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[-1, 6]], [[1, 8]], [[1, 2]], [[-1, 8]], [[-1, 2]], [[1, 6]], [[1, 8]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 8]], [[1, 6]], [[1, 8]], [[1, 2]], [[1, 6]], [[1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 6]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[-1, 7]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[-1, 3]], [[1, 9]], [[1, 1]], [[1, 7]], [[-1, 9]], [[1, 9]], [[-1, 7]], [[1, 3]], [[-1, 8]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 9]], [[1, 1]], [[-1, 9]], [[1, 3]], [[-1, 9]], [[-1, 7]], [[-1, 7]], [[-1, 4]], [[1, 9]], [[1, 1]], [[-1, 6]], [[-1, 7]], [[1, 4]], [[-1, 9]], [[1, 9]], [[1, 8]], [[1, 7]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[1, 7]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 6]], [[-1, 3]]]}
  • id: 31628007
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  • id: 31628008
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 158, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.a1', 'kernel_order': 48, 'label': '960.10116.1av6', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 5]], [[1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 4]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 4]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 8]], [[-1, 4]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 8]], [[1, 2]], [[-1, 6]], [[1, 4]], [[1, 6]], [[-1, 2]], [[-1, 2]], [[1, 6]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 0]], [[-1, 0]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 8]], [[1, 1]], [[-1, 9]], [[-1, 3]], [[1, 3]], [[1, 7]], [[1, 7]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 9]], [[-1, 7]], [[1, 9]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[-1, 3]], [[-1, 2]], [[1, 3]], [[-1, 9]], [[-1, 4]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 7]], [[-1, 6]], [[-1, 7]], [[1, 7]], [[-1, 7]], [[-1, 3]], [[1, 9]], [[-1, 8]], [[1, 7]], [[-1, 1]], [[1, 1]], [[1, 8]], [[1, 9]], [[-1, 9]], [[1, 6]], [[-1, 9]], [[1, 9]], [[1, 3]], [[1, 2]], [[1, 1]], [[-1, 1]], [[-1, 7]], [[-1, 3]], [[1, 1]], [[1, 4]], [[1, 8]], [[1, 8]], [[-1, 6]], [[-1, 8]], [[-1, 4]], [[1, 1]], [[1, 7]], [[-1, 6]], [[1, 9]], [[-1, 3]], [[1, 2]], [[-1, 9]], [[-1, 8]], [[-1, 1]], [[1, 7]], [[1, 9]], [[1, 3]], [[-1, 9]], [[-1, 7]], [[1, 3]], [[1, 4]], [[-1, 2]], [[-1, 7]], [[-1, 3]], [[1, 6]], [[-1, 1]], [[1, 1]], [[1, 2]], [[1, 6]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 1]], [[1, 4]], [[1, 6]], [[1, 9]], [[-1, 3]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[1, 1]], [[1, 3]], [[1, 7]], [[-1, 9]], [[1, 8]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 7]], [[-1, 9]], [[1, 3]], [[1, 7]], [[1, 1]], [[-1, 3]], [[1, 9]], [[1, 2]], [[-1, 3]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[-1, 7]], [[1, 3]], [[-1, 1]], [[-1, 4]], [[-1, 8]], [[1, 7]], [[-1, 9]], [[1, 1]], [[-1, 2]], [[-1, 6]], [[-1, 4]], [[1, 6]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 6]], [[1, 2]], [[-1, 8]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[1, 4]], [[1, 6]], [[1, 6]], [[1, 2]], [[-1, 6]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 7]], [[1, 1]], [[1, 9]], [[-1, 1]], [[-1, 7]], [[1, 7]], [[-1, 9]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 7]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 9]], [[-1, 1]], [[1, 6]], [[-1, 1]], [[1, 1]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 7]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 9]], [[1, 9]], [[-1, 8]], [[-1, 3]], [[-1, 7]], [[-1, 2]], [[1, 9]], [[1, 8]], [[1, 3]], [[-1, 3]], [[-1, 6]], [[-1, 9]], [[-1, 4]], [[1, 4]], [[1, 7]], [[-1, 9]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[1, 7]], [[1, 2]], [[1, 1]]]}
  • id: 31628009
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 960, 'counter': 159, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.x1.a1', 'kernel_order': 48, 'label': '960.10116.1av7', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[-1, 0]], [[1, 5]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 0]], [[1, 5]], [[1, 5]], [[-1, 0]], [[1, 0]], [[1, 5]], [[1, 4]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 6]], [[1, 8]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 4]], [[1, 6]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 8]], [[-1, 4]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 8]], [[1, 2]], [[-1, 6]], [[1, 4]], [[1, 6]], [[-1, 2]], [[-1, 2]], [[1, 6]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 8]], [[-1, 1]], [[1, 9]], [[1, 3]], [[-1, 3]], [[-1, 7]], [[-1, 7]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 9]], [[1, 7]], [[-1, 9]], [[1, 9]], [[-1, 3]], [[1, 7]], [[1, 3]], [[-1, 2]], [[-1, 3]], [[1, 9]], [[-1, 4]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 7]], [[-1, 6]], [[1, 7]], [[-1, 7]], [[1, 7]], [[1, 3]], [[-1, 9]], [[-1, 8]], [[-1, 7]], [[1, 1]], [[-1, 1]], [[1, 8]], [[-1, 9]], [[1, 9]], [[1, 6]], [[1, 9]], [[-1, 9]], [[-1, 3]], [[1, 2]], [[-1, 1]], [[1, 1]], [[1, 7]], [[1, 3]], [[-1, 1]], [[1, 4]], [[1, 8]], [[1, 8]], [[-1, 6]], [[-1, 8]], [[-1, 4]], [[-1, 1]], [[-1, 7]], [[-1, 6]], [[-1, 9]], [[1, 3]], [[1, 2]], [[1, 9]], [[-1, 8]], [[1, 1]], [[-1, 7]], [[-1, 9]], [[-1, 3]], [[1, 9]], [[1, 7]], [[-1, 3]], [[1, 4]], [[-1, 2]], [[1, 7]], [[1, 3]], [[1, 6]], [[1, 1]], [[-1, 1]], [[1, 2]], [[1, 6]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 1]], [[1, 4]], [[1, 6]], [[-1, 9]], [[1, 3]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[-1, 7]], [[1, 9]], [[1, 8]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[1, 7]], [[1, 9]], [[-1, 3]], [[-1, 7]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[1, 2]], [[1, 3]], [[1, 7]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 3]], [[1, 1]], [[-1, 4]], [[-1, 8]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[-1, 2]], [[-1, 6]], [[-1, 4]], [[1, 6]], [[1, 4]], [[1, 2]], [[-1, 6]], [[1, 6]], [[1, 2]], [[-1, 8]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[1, 4]], [[1, 6]], [[1, 6]], [[1, 2]], [[-1, 6]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 7]], [[-1, 1]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 7]], [[1, 9]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 7]], [[1, 9]], [[-1, 3]], [[1, 3]], [[-1, 9]], [[1, 1]], [[1, 6]], [[1, 1]], [[-1, 1]], [[1, 7]], [[-1, 1]], [[1, 3]], [[1, 7]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 9]], [[-1, 9]], [[-1, 8]], [[1, 3]], [[1, 7]], [[-1, 2]], [[-1, 9]], [[1, 8]], [[-1, 3]], [[1, 3]], [[-1, 6]], [[1, 9]], [[-1, 4]], [[1, 4]], [[-1, 7]], [[1, 9]], [[1, 9]], [[-1, 7]], [[1, 1]], [[-1, 7]], [[1, 2]], [[-1, 1]]]}
  • id: 31628011
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  • id: 31628054
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  • id: 31628165
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  • id: 31628177
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  • id: 31628188
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  • id: 31628199
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  • id: 31628210
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  • id: 31628221
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  • id: 31628232
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  • id: 31627944
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  • id: 31627955
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  • id: 31627966
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  • id: 31627977
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  • id: 31627988
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  • id: 31627999
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  • id: 31628010
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  • id: 31628021
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  • id: 31628032
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  • id: 31628043
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  • id: 31628055
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  • id: 31628066
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  • id: 31628077
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  • id: 31628088
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  • id: 31628099
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  • id: 31628110
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  • id: 31628121
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  • id: 31628132
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  • id: 31628143
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  • id: 31628154
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  • id: 31628166
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  • id: 31628168
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  • id: 31628169
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  • id: 31628170
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  • id: 31628171
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  • id: 31628172
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  • id: 31628173
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  • id: 31628174
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  • id: 31628175
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  • id: 31628176
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  • id: 31628178
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  • id: 31628012
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  • id: 31628092
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  • id: 31628093
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  • id: 31628094
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  • id: 31628095
    {'center': '4.m1.a1', 'center_index': 4, 'center_order': 240, 'counter': 236, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '80.48', 'image_order': 80, 'indicator': 0, 'kernel': '80.h1.b1', 'kernel_order': 12, 'label': '960.10116.2aa4', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[-2, 5]], [[2, 5]], [[2, 5]], [[-2, 5]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-2, 6]], [[2, 8]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[2, 2]], [[-2, 4]], [[-2, 8]], [[2, 4]], [[2, 6]], [[-2, 8]], [[-2, 4]], [[2, 2]], [[-2, 6]], [[-2, 2]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[2, 8]], [[-2, 2]], [[2, 4]], [[-2, 8]], [[-2, 2]], [[2, 4]], [[-2, 4]], [[-2, 6]], [[2, 6]], [[2, 8]], [[-2, 8]], [[2, 8]], [[-2, 2]], [[2, 6]], [[2, 2]], [[2, 2]], [[2, 4]], [[-2, 6]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 9]], [[2, 9]], [[-2, 3]], [[2, 9]], [[2, 7]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 7]], [[2, 9]], [[-2, 1]], [[2, 7]], [[-2, 9]], [[2, 3]], [[-2, 1]], [[2, 7]], [[2, 9]], [[-2, 7]], [[2, 1]], [[-2, 9]], [[2, 7]], [[-2, 1]], [[-2, 1]], [[-2, 9]], [[2, 3]], [[-2, 3]], [[2, 3]], [[2, 1]], [[-2, 3]], [[-2, 7]], [[-2, 7]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 8]], [[2, 2]], [[2, 6]], [[-2, 8]], [[2, 8]], [[-2, 6]], [[2, 4]], [[-2, 4]], [[-2, 2]], [[-2, 4]], [[2, 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]], [[-2, 6]], [[-2, 8]], [[2, 2]], [[-2, 8]], [[2, 6]], [[2, 6]], [[2, 2]], [[2, 4]], [[2, 8]], [[-2, 4]], [[-2, 6]], [[-2, 2]], [[-2, 4]], [[2, 4]], [[-2, 2]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31628096
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  • id: 31628097
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  • id: 31628098
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  • id: 31628100
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  • id: 31628101
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  • id: 31628102
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  • id: 31628103
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  • id: 31628104
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  • id: 31628105
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  • id: 31628106
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  • id: 31628107
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  • id: 31628108
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  • id: 31628109
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  • id: 31628111
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  • id: 31628112
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  • id: 31628113
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  • id: 31628114
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  • id: 31628115
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  • id: 31628116
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  • id: 31628117
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  • id: 31628118
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  • id: 31628119
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  • id: 31628120
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  • id: 31628122
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  • id: 31628123
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  • id: 31628124
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  • id: 31628125
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  • id: 31628126
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  • id: 31628127
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  • id: 31628128
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  • id: 31628129
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  • id: 31628130
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  • id: 31628131
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  • id: 31628133
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  • id: 31628134
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  • id: 31628135
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  • id: 31628136
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  • id: 31628137
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  • id: 31628138
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  • id: 31628139
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  • id: 31628140
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  • id: 31628141
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  • id: 31628142
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  • id: 31628144
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  • id: 31628013
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  • id: 31628014
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  • id: 31628015
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  • id: 31628016
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  • id: 31628017
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  • id: 31628018
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  • id: 31628019
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  • id: 31628020
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  • id: 31628022
    {'center': '4.m1.a1', 'center_index': 4, 'center_order': 240, 'counter': 170, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.b1', 'kernel_order': 60, 'label': '960.10116.2i2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 0]], [[2, 1]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31628023
    {'center': '4.m1.a1', 'center_index': 4, 'center_order': 240, 'counter': 171, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1.a1', 'kernel_order': 60, 'label': '960.10116.2j1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[2, 1]], [[2, 0]], [[2, 0]], [[-2, 1]], [[2, 0]], [[-2, 1]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31628024
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  • id: 31628025
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  • id: 31628026
    {'center': '4.m1.a1', 'center_index': 4, 'center_order': 240, 'counter': 174, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.h1.b1', 'kernel_order': 60, 'label': '960.10116.2k2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31628027
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  • id: 31628028
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  • id: 31628029
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  • id: 31628030
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  • id: 31628031
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  • id: 31628033
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  • id: 31628034
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  • id: 31628035
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  • id: 31628036
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  • id: 31628037
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  • id: 31628038
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  • id: 31628039
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  • id: 31628040
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  • id: 31628041
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  • id: 31628042
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  • id: 31628044
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  • id: 31628045
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  • id: 31628046
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  • id: 31628047
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  • id: 31628048
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  • id: 31628049
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  • id: 31628050
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  • id: 31628051
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  • id: 31628052
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  • id: 31628053
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  • id: 31628056
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  • id: 31628057
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  • id: 31628058
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  • id: 31628059
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  • id: 31628060
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  • id: 31628061
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  • id: 31628062
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  • id: 31628063
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  • id: 31628064
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  • id: 31628065
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  • id: 31628067
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  • id: 31628068
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  • id: 31628069
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  • id: 31628070
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  • id: 31628071
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  • id: 31628072
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  • id: 31628073
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  • id: 31628074
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  • id: 31628075
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  • id: 31628076
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  • id: 31628078
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  • id: 31628079
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  • id: 31628080
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  • id: 31628081
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  • id: 31628082
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  • id: 31628083
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  • id: 31628084
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  • id: 31628085
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  • id: 31628086
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  • id: 31628087
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  • id: 31628089
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  • id: 31628090
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  • id: 31628091
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  • id: 31628145
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  • id: 31628146
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  • id: 31628147
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  • id: 31628148
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  • id: 31628149
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  • id: 31628150
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  • id: 31628151
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  • id: 31628152
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  • id: 31628153
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  • id: 31628155
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  • id: 31628157
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  • id: 31628158
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  • id: 31628159
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  • id: 31628160
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  • id: 31628161
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  • id: 31628162
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  • id: 31628163
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 40, 'counter': 298, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '480.1160', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10116.4f6', 'nt': [120, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 5]], [[-4, 5]], [[4, 5]], [[-4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[4, 8]], [[-4, 2]], [[-4, 6]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[4, 4]], [[4, 8]], [[-4, 6]], [[-4, 8]], [[4, 2]], [[4, 6]], [[-4, 8]], [[-4, 4]], [[4, 2]], [[-4, 4]], [[4, 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]], [[2, 5]], [[-2, 5]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 6]], [[-2, 4]], [[-2, 8]], [[4, 1]], [[4, 9]], [[4, 3]], [[4, 3]], [[-4, 7]], [[4, 7]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[-4, 9]], [[-4, 7]], [[4, 9]], [[-4, 9]], [[-4, 3]], [[4, 7]], [[-4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 6]], [[2, 4]], [[2, 2]], [[-2, 6]], [[-2, 6]], [[-2, 2]], [[2, 8]], [[2, 8]], [[2, 4]], [[-2, 8]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 7]], [[-2, 1]], [[-2, 9]], [[2, 1]], [[2, 7]], [[-2, 7]], [[2, 9]], [[2, 3]], [[2, 1]], [[2, 3]], [[-2, 7]], [[-2, 9]], [[-2, 3]], [[-2, 3]], [[2, 9]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31628164
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 40, 'counter': 299, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '480.1160', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10116.4f7', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 5]], [[4, 5]], [[-4, 5]], [[4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[4, 8]], [[-4, 2]], [[-4, 6]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[4, 4]], [[4, 8]], [[-4, 6]], [[-4, 8]], [[4, 2]], [[4, 6]], [[-4, 8]], [[-4, 4]], [[4, 2]], [[-4, 4]], [[4, 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]], [[-2, 5]], [[2, 5]], [[2, 5]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 6]], [[-2, 4]], [[-2, 8]], [[-4, 1]], [[-4, 9]], [[-4, 3]], [[-4, 3]], [[4, 7]], [[-4, 7]], [[4, 1]], [[4, 1]], [[-4, 1]], [[4, 9]], [[4, 7]], [[-4, 9]], [[4, 9]], [[4, 3]], [[-4, 7]], [[4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 6]], [[2, 4]], [[2, 2]], [[-2, 6]], [[-2, 6]], [[-2, 2]], [[2, 8]], [[2, 8]], [[2, 4]], [[-2, 8]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 7]], [[2, 1]], [[2, 9]], [[-2, 1]], [[-2, 7]], [[2, 7]], [[-2, 9]], [[-2, 3]], [[-2, 1]], [[-2, 3]], [[2, 7]], [[2, 9]], [[2, 3]], [[2, 3]], [[-2, 9]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 31628167
    {'center': '24.b1.a1', 'center_index': 24, 'center_order': 40, 'counter': 300, 'cyclotomic_n': 20, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '960.10116', 'group_counter': 10116, 'group_order': 960, 'image': None, 'image_isoclass': '480.1160', 'image_order': 480, 'indicator': 0, 'kernel': '480.a1.a1', 'kernel_order': 2, 'label': '960.10116.4f8', 'nt': [120, 8], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 5]], [[-4, 5]], [[4, 5]], [[-4, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 6]], [[-4, 2]], [[4, 8]], [[4, 4]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 8]], [[-4, 6]], [[-4, 2]], [[4, 4]], [[4, 2]], [[-4, 8]], [[-4, 4]], [[4, 2]], [[4, 6]], [[-4, 8]], [[4, 6]], [[-4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 5]], [[-2, 5]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8]], [[-2, 4]], [[2, 6]], [[2, 2]], [[4, 9]], [[4, 1]], [[4, 7]], [[4, 7]], [[-4, 3]], [[4, 3]], [[-4, 9]], [[-4, 9]], [[4, 9]], [[-4, 1]], [[-4, 3]], [[4, 1]], [[-4, 1]], [[-4, 7]], [[4, 3]], [[-4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[-2, 4]], [[-2, 6]], [[-2, 8]], [[2, 4]], [[2, 4]], [[2, 8]], [[-2, 2]], [[-2, 2]], [[-2, 6]], [[2, 2]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 9]], [[-2, 1]], [[2, 9]], [[2, 3]], [[-2, 3]], [[2, 1]], [[2, 7]], [[2, 9]], [[2, 7]], [[-2, 3]], [[-2, 1]], [[-2, 7]], [[-2, 7]], [[2, 1]], [[-2, 9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

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

  
  
  • id: 112319269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 960, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '960.10116.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '960.10116', 'subgroup_hash': 10116, 'subgroup_order': 960, 'subgroup_tex': 'D_4:S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319380
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 480, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.807', 'subgroup_hash': 807, 'subgroup_order': 480, 'subgroup_tex': 'C_{60}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 480, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.807', 'subgroup_hash': 807, 'subgroup_order': 480, 'subgroup_tex': 'C_{60}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 480, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.760', 'subgroup_hash': 760, 'subgroup_order': 480, 'subgroup_tex': 'C_3:(D_4\\times C_{20})', 'supersolvable': True, 'sylow': 0}
  • id: 112319713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 480, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.760', 'subgroup_hash': 760, 'subgroup_order': 480, 'subgroup_tex': 'C_3:(D_4\\times C_{20})', 'supersolvable': True, 'sylow': 0}
  • id: 112319824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 480, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.801', 'subgroup_hash': 801, 'subgroup_order': 480, 'subgroup_tex': 'C_{30}:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 480, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': '480.801', 'subgroup_hash': 801, 'subgroup_order': 480, 'subgroup_tex': 'C_{30}:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 480, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.756', 'subgroup_hash': 756, 'subgroup_order': 480, 'subgroup_tex': 'C_5\\times C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 480, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.756', 'subgroup_hash': 756, 'subgroup_order': 480, 'subgroup_tex': 'C_5\\times C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 480, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '480.1155', 'subgroup_hash': 1155, 'subgroup_order': 480, 'subgroup_tex': 'C_{60}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 480, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.923', 'subgroup_hash': 923, 'subgroup_order': 480, 'subgroup_tex': 'D_4\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 480, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.813', 'subgroup_hash': 813, 'subgroup_order': 480, 'subgroup_tex': 'C_3:C_{20}\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319303
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 480, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.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': '480.750', 'subgroup_hash': 750, 'subgroup_order': 480, 'subgroup_tex': 'C_4\\times S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 480, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.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': '480.771', 'subgroup_hash': 771, 'subgroup_order': 480, 'subgroup_tex': '(C_4\\times S_3):C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 480, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.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': '480.747', 'subgroup_hash': 747, 'subgroup_order': 480, 'subgroup_tex': 'C_{60}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 480, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.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': '480.766', 'subgroup_hash': 766, 'subgroup_order': 480, 'subgroup_tex': 'C_3:(Q_8\\times C_{20})', 'supersolvable': True, 'sylow': 0}
  • id: 112319347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 160, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '960.10116.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '320.1519', 'subgroup_hash': 1519, 'subgroup_order': 320, 'subgroup_tex': 'C_4\\times D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.174', 'subgroup_hash': 174, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.174', 'subgroup_hash': 174, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 240, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '240.185', 'subgroup_hash': 185, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 240, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '240.185', 'subgroup_hash': 185, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319403
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 240, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '240.82', 'subgroup_hash': 82, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2:C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 240, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.82', 'subgroup_hash': 82, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2:C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.173', 'subgroup_hash': 173, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.173', 'subgroup_hash': 173, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.173', 'subgroup_hash': 173, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319458
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.173', 'subgroup_hash': 173, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319469
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.64', 'subgroup_hash': 64, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319480
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '240.64', 'subgroup_hash': 64, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 240, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.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': '240.186', 'subgroup_hash': 186, 'subgroup_order': 240, 'subgroup_tex': 'D_4\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319503
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 240, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.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': '240.166', 'subgroup_hash': 166, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319514
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 240, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.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': '240.166', 'subgroup_hash': 166, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.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': '240.59', 'subgroup_hash': 59, 'subgroup_order': 240, 'subgroup_tex': 'D_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.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': '240.59', 'subgroup_hash': 59, 'subgroup_order': 240, 'subgroup_tex': 'D_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 240, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.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': '240.166', 'subgroup_hash': 166, 'subgroup_order': 240, 'subgroup_tex': 'D_6\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 240, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.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': '240.81', 'subgroup_hash': 81, 'subgroup_order': 240, 'subgroup_tex': 'C_4\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': True, 'core_order': 240, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 240, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.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': '240.83', 'subgroup_hash': 83, 'subgroup_order': 240, 'subgroup_tex': 'C_4:C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 240, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 240, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.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': '240.165', 'subgroup_hash': 165, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 240, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.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': '240.58', 'subgroup_hash': 58, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 240, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.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': '240.57', 'subgroup_hash': 57, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.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': '240.57', 'subgroup_hash': 57, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 240, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.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': '240.56', 'subgroup_hash': 56, 'subgroup_order': 240, 'subgroup_tex': 'C_{12}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.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': '240.57', 'subgroup_hash': 57, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.4.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.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': '240.57', 'subgroup_hash': 57, 'subgroup_order': 240, 'subgroup_tex': 'C_{30}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 53, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 54, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 55, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 56, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 57, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 58, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 59, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 240, 'counter': 60, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.4.x1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.170', 'subgroup_hash': 170, 'subgroup_order': 240, 'subgroup_tex': 'C_{20}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 192, 'counter': 61, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '960.10116.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1095', 'subgroup_hash': 1095, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 160, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '160.179', 'subgroup_hash': 179, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.179', 'subgroup_hash': 179, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.179', 'subgroup_hash': 179, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.179', 'subgroup_hash': 179, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.179', 'subgroup_hash': 179, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 80, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.175', 'subgroup_hash': 175, 'subgroup_order': 160, 'subgroup_tex': 'C_2\\times C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 80, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '160.175', 'subgroup_hash': 175, 'subgroup_order': 160, 'subgroup_tex': 'C_2\\times C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.178', 'subgroup_hash': 178, 'subgroup_order': 160, 'subgroup_tex': 'C_4^2:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '160.178', 'subgroup_hash': 178, 'subgroup_order': 160, 'subgroup_tex': 'C_4^2:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '160.231', 'subgroup_hash': 231, 'subgroup_order': 160, 'subgroup_tex': 'C_{10}.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 112319859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '160.179', 'subgroup_hash': 179, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 80, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '160.175', 'subgroup_hash': 175, 'subgroup_order': 160, 'subgroup_tex': 'C_2\\times C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '160.178', 'subgroup_hash': 178, 'subgroup_order': 160, 'subgroup_tex': 'C_4^2:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '160.180', 'subgroup_hash': 180, 'subgroup_order': 160, 'subgroup_tex': 'Q_8\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 80, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '160.180', 'subgroup_hash': 180, 'subgroup_order': 160, 'subgroup_tex': 'Q_8\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319864
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 120, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.47', 'subgroup_hash': 47, 'subgroup_order': 120, 'subgroup_tex': 'C_2^2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319865
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 120, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.b1', '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': '120.47', 'subgroup_hash': 47, 'subgroup_order': 120, 'subgroup_tex': 'C_2^2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 120, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.45', 'subgroup_hash': 45, 'subgroup_order': 120, 'subgroup_tex': 'C_{10}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319868
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 120, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 120, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 120, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 120, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.b1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 120, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': True, 'core_order': 120, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': True, 'core_order': 120, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.b1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.b1', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 120, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.l1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.25', 'subgroup_hash': 25, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319276
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.m1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 120, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.32', 'subgroup_hash': 32, 'subgroup_order': 120, 'subgroup_tex': 'D_4\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 112319280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 120, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.32', 'subgroup_hash': 32, 'subgroup_order': 120, 'subgroup_tex': 'D_4\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 112319282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 120, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.32', 'subgroup_hash': 32, 'subgroup_order': 120, 'subgroup_tex': 'D_4\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 112319283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 120, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.32', 'subgroup_hash': 32, 'subgroup_order': 120, 'subgroup_tex': 'D_4\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 112319284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 120, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.21', 'subgroup_hash': 21, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.21', 'subgroup_hash': 21, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.21', 'subgroup_hash': 21, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 120, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.8.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.21', 'subgroup_hash': 21, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319298
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.r1.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': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319299
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319300
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.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': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319304
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319305
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.8.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1.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': '120.22', 'subgroup_hash': 22, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 96, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 96, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 96, 'counter': 134, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 96, 'counter': 135, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 96, 'counter': 136, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.129', 'subgroup_hash': 129, 'subgroup_order': 96, 'subgroup_tex': 'C_6:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 96, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.129', 'subgroup_hash': 129, 'subgroup_order': 96, 'subgroup_tex': 'C_6:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 96, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.84', 'subgroup_hash': 84, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 96, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.84', 'subgroup_hash': 84, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 96, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.210', 'subgroup_hash': 210, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 96, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 96, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 96, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.78', 'subgroup_hash': 78, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 96, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.99', 'subgroup_hash': 99, 'subgroup_order': 96, 'subgroup_tex': '(C_4\\times S_3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 96, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.75', 'subgroup_hash': 75, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 96, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.10.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 112319322
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 80, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 80, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 80, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '80.21', 'subgroup_hash': 21, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 80, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.21', 'subgroup_hash': 21, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 80, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.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': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319328
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 80, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.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': '12.4', '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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 80, 'counter': 153, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1.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': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.46', 'subgroup_hash': 46, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319332
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319333
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '80.21', 'subgroup_hash': 21, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '80.21', 'subgroup_hash': 21, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319340
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '80.21', 'subgroup_hash': 21, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.21', 'subgroup_hash': 21, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319343
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 40, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319348
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.47', 'subgroup_hash': 47, 'subgroup_order': 80, 'subgroup_tex': 'Q_8\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319351
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319352
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1.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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319353
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319354
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1.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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.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': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319357
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 40, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319359
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319360
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.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': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319361
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319362
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.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': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.e1', 'outer_equivalence': False, 'perfect': False, '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': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.f1', 'outer_equivalence': False, 'perfect': False, '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': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319367
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.g1', 'outer_equivalence': False, 'perfect': False, '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': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 40, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.12.x1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.h1', 'outer_equivalence': False, 'perfect': False, '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': '80.48', 'subgroup_hash': 48, 'subgroup_order': 80, 'subgroup_tex': 'D_4:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 32, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '960.10116.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.198', 'subgroup_hash': 198, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 112319371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 60, 'counter': 191, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.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': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319372
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 60, 'counter': 192, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319373
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 60, 'counter': 193, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', '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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 194, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 195, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 196, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 197, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319378
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 198, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319382
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 200, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319383
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 60, 'counter': 201, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319384
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 60, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319385
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 60, 'counter': 203, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319386
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 204, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319387
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 205, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319388
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 206, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319389
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 60, 'counter': 207, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.16.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319390
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 60, 'counter': 208, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.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': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319391
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 60, 'counter': 209, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.b1', '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': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 30, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319396
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319397
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 30, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319398
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 30, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 30, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.11', 'subgroup_hash': 11, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319402
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 219, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319404
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 30, 'counter': 220, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.16.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
  • id: 112319405
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 30, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319406
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 222, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 223, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 48, 'counter': 224, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 48, 'counter': 225, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 48, 'counter': 226, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 48, 'counter': 227, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 228, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319413
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 229, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 230, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 231, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 232, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319418
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 233, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 48, 'counter': 234, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 48, 'counter': 235, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 48, 'counter': 236, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 237, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 238, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 48, 'counter': 239, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319426
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 48, 'counter': 240, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': True, 'core_order': 48, 'counter': 241, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 48, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 48, 'counter': 245, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 48, 'counter': 246, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': True, 'core_order': 48, 'counter': 247, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319434
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 248, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319435
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 249, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 250, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319438
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 48, 'counter': 251, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 252, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 253, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 48, 'counter': 254, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 255, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 256, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.20.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 257, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 258, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 259, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 260, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 261, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 262, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 263, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': False, 'core_order': 48, 'counter': 264, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '960.10116.20.x1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.x1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.39', 'subgroup_hash': 39, 'subgroup_order': 48, 'subgroup_tex': 'D_4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 40, 'counter': 265, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 40, 'counter': 266, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', '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': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 40, 'counter': 267, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.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': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 40, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 40, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 40, 'counter': 270, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.b1', '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 40, 'counter': 271, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.e1.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 40, 'counter': 272, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319462
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 40, 'counter': 273, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 40, 'counter': 274, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 40, 'counter': 275, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.24.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 20, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 20, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319482
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.e1', 'outer_equivalence': False, 'perfect': False, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.f1', 'outer_equivalence': False, 'perfect': False, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.g1', 'outer_equivalence': False, 'perfect': False, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.o1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.h1', 'outer_equivalence': False, 'perfect': False, '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': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.e1', 'outer_equivalence': False, 'perfect': False, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.f1', 'outer_equivalence': False, 'perfect': False, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.g1', 'outer_equivalence': False, 'perfect': False, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.p1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.h1', 'outer_equivalence': False, 'perfect': False, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.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': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 20, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319511
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319513
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 20, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 32, 'counter': 320, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319520
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 16, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319521
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 16, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 16, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 16, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.30.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319531
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 30, 'counter': 335, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 30, 'counter': 336, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 30, 'counter': 337, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 15, 'counter': 338, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319535
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 15, 'counter': 339, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319537
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 15, 'counter': 340, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.32.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 15, 'counter': 341, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.32.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 112319539
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 15, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319540
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 15, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 24, 'counter': 344, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 24, 'counter': 345, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 24, 'counter': 346, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 24, 'counter': 347, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', '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: 112319545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 24, 'counter': 348, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', '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: 112319546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 24, 'counter': 349, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', '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: 112319548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 24, 'counter': 350, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', '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: 112319549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 24, 'counter': 351, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', '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: 112319550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': True, 'core_order': 24, 'counter': 352, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': True, 'core_order': 24, 'counter': 353, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 354, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 355, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 356, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 357, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 24, 'counter': 358, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 359, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 360, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 361, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 362, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 363, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 364, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 365, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 366, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.l1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.l1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 367, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 368, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 369, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 370, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 371, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 372, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 373, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 374, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.m1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.m1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 24, 'counter': 375, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 24, 'counter': 376, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 24, 'counter': 377, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 24, 'counter': 378, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 379, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 380, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 381, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 24, 'counter': 382, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 383, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 384, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 385, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 24, 'counter': 386, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.40.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319600
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.40.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 20, 'counter': 399, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.48.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': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 400, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.48.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': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 401, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.48.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 402, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.48.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 403, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.48.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319608
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 404, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319609
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 20, 'counter': 405, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319610
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 20, 'counter': 406, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '960.10116.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319611
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 20, 'counter': 407, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '960.10116.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319616
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 411, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319617
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 10, 'counter': 412, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319618
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 10, 'counter': 413, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319619
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 414, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319620
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 415, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319623
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 10, 'counter': 418, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319624
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 10, 'counter': 419, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319626
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 420, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319627
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 421, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319628
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 422, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319629
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 423, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319630
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319633
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 427, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319634
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 10, 'counter': 428, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319635
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 10, 'counter': 429, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 112319637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 16, 'counter': 430, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 16, 'counter': 431, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 16, 'counter': 432, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 16, 'counter': 433, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 16, 'counter': 434, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 16, 'counter': 435, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': True, 'core_order': 16, 'counter': 436, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319646
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319648
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319649
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319650
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319653
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319654
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.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': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 8, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319660
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319661
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319662
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 8, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 8, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.60.x1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.x1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319684
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 15, 'counter': 473, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '960.10116.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.198', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 198, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 112319685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 12, 'counter': 474, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.52', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 52, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_{10}', '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: 112319686
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 12, 'counter': 475, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319687
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 12, 'counter': 476, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 112319688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 477, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', '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: 112319689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 478, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', '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: 112319690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 479, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', '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: 112319692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 480, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', '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: 112319693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 481, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 482, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319695
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 483, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', '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: 112319696
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 12, 'counter': 484, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.80.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', '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: 112319697
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 12, 'counter': 485, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319698
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 160, 'characteristic': False, 'core_order': 12, 'counter': 486, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319699
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 487, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319700
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 488, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319701
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 489, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319703
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 12, 'counter': 490, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.80.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '80.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319704
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 12, 'counter': 491, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.80.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319705
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 12, 'counter': 492, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.80.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319709
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 496, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.80.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319710
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319711
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319712
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319717
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 502, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.80.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319718
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 503, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.80.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 112319719
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 6, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.80.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319720
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 10, 'counter': 505, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.215', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 215, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319721
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 10, 'counter': 506, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.206', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 206, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319722
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 10, 'counter': 507, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.210', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 210, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319723
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 5, 'counter': 508, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319724
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 5, 'counter': 509, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.96.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319726
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 5, 'counter': 510, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.96.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319727
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 5, 'counter': 511, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.96.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319728
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 5, 'counter': 512, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319729
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 5, 'counter': 513, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.96.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 112319730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 8, 'counter': 514, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319731
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 8, 'counter': 515, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 8, 'counter': 516, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319733
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 8, 'counter': 517, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 8, 'counter': 518, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 8, 'counter': 519, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319737
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 8, 'counter': 520, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 112319738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 8, 'counter': 521, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.22', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 8, 'counter': 522, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.22', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 8, 'counter': 523, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.22', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 240, 'characteristic': False, 'core_order': 8, 'counter': 524, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.120.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.22', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 112319743
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 4, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319744
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 4, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319746
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319749
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319752
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319753
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319755
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.o1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.o1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319766
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319767
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319770
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319771
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319772
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319773
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.p1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.p1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319775
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.r1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 112319784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319785
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319786
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319789
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 4, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.120.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319790
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 6, 'counter': 569, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.231', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 231, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}.C_2^4', '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: 112319792
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 6, 'counter': 570, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.228', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 228, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], '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: 112319793
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 6, 'counter': 571, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.231', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 231, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}.C_2^4', '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: 112319794
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 572, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.160.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319795
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 573, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.160.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319796
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 574, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.160.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319797
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 575, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.160.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 112319798
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.160.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319799
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 3, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.160.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 112319800
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 5, 'counter': 578, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '960.10116.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1095', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1095, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.D_6', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 112319801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 4, 'counter': 579, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.206', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 206, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 112319803
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 580, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{20}', '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: 112319804
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 581, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.240.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{20}', '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: 112319805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 582, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.240.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{20}', '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: 112319806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 583, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10116.240.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{20}', '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: 112319807
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 584, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{20}', '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: 112319808
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 4, 'counter': 585, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.166', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 166, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{20}', '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: 112319809
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 4, 'counter': 586, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '960.10116.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.170', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319810
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 4, 'counter': 587, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '960.10116.240.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '240.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.170', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319811
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319815
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 591, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319816
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 2, 'counter': 592, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319817
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 2, 'counter': 593, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319818
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 594, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319819
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 595, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319821
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319822
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 2, 'counter': 598, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 320, 'characteristic': False, 'core_order': 2, 'counter': 599, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319826
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 600, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319827
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 601, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319828
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 602, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319829
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 603, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319831
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.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': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319832
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '960.10116.240.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 112319833
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 607, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319834
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 608, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319835
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 609, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.240.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 112319837
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 3, 'counter': 610, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '960.10116.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '320.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '320.1519', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1519, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_4:C_{10}', 'simple': True, 'solvable': True, 'special_labels': ['L2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 112319838
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 2, 'counter': 611, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.1160', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1160, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{60}.C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319839
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 2, 'counter': 612, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.1151', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1151, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{60}:C_2^3', '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: 112319840
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 2, 'counter': 613, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.10116.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.1155', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1155, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{60}.C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 112319841
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 112319842
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.480.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 112319843
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 616, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.480.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, '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: 112319844
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 1, 'counter': 617, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.480.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, '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: 112319845
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 112319846
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '960.10116.480.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.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': 480, '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: 112319848
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.10116', 'ambient_counter': 10116, 'ambient_order': 960, 'ambient_tex': 'D_4:S_3\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 1, 'counter': 620, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '960.10116.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '960.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '960.10116', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10116, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 960, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3\\times C_{20}', '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: 112319269
    {'ambient': '960.10116', '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': '24.b1.a1', 'complements': ['960.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.d1.b1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6974, 3928, 5877, 6132, 6203, 5944, 6119, 3778], 'generators': [1, 192, 480, 4, 488, 640, 2, 240], 'label': '960.10116.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.b1', '2.b1.a1', '2.c1.b1', '2.c1.a1', '2.d1.b1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '24.14', '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': '24.14'}
  • id: 112319270
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.e1.a1', '4.e1.b1', '4.g1.a1', '4.i1.a1', '4.q1.a1', '4.x1.a1', '4.x1.b1', '4.x1.c1', '4.x1.d1', '4.x1.e1', '4.x1.f1', '4.x1.g1', '4.x1.h1', '6.f1.a1', '10.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8914, 6940, 3027, 3495, 8219, 3642, 3197, 6893], 'generators': [1, 488, 404, 480, 2, 640, 192], 'label': '960.10116.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.a1.a1', '4.e1.b1', '4.e1.a1', '4.g1.a1', '4.i1.a1', '4.q1.a1', '4.x1.c1', '4.x1.d1', '4.x1.g1', '4.x1.h1', '4.x1.a1', '4.x1.b1', '4.x1.e1', '4.x1.f1', '10.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319271
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1', '120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.x1.a1', '4.x1.d1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.g1.a1', '24.p1.a1', '40.m1.a1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 526, 1197, 7531, 2099, 1430, 8690], 'generators': [2, 192, 488, 404, 640], 'label': '960.10116.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.e1.a1', '4.x1.d1', '4.x1.a1'], 'normal_contains': ['16.c1.a1', '16.f1.a1', '16.g1.a1', '40.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319272
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.d1', '120.m1.c1', '120.t1.a1', '120.t1.b1', '120.n1.b1', '120.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.x1.b1', '4.x1.c1'], 'contains': ['16.c1.a1', '16.f1.b1', '16.g1.c1', '24.p1.b1', '40.m1.b1'], 'core': '8.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 593, 2116, 7531, 2099, 364, 8343], 'generators': [2, 192, 488, 884, 640], 'label': '960.10116.8.m1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.b1', 'normal_contained_in': ['4.e1.a1', '4.x1.c1', '4.x1.b1'], 'normal_contains': ['16.c1.a1', '16.f1.b1', '16.g1.c1', '40.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319273
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1', '120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.x1.f1', '4.x1.g1'], 'contains': ['16.c1.b1', '16.f1.a1', '16.g1.c1', '24.p1.c1', '40.m1.c1'], 'core': '8.m1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 1993, 2884, 7531, 2099, 1632, 7778], 'generators': [482, 192, 488, 404, 640], 'label': '960.10116.8.m1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.c1', 'normal_contained_in': ['4.e1.a1', '4.x1.g1', '4.x1.f1'], 'normal_contains': ['16.c1.b1', '16.f1.a1', '16.g1.c1', '40.m1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319274
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.d1', '120.m1.c1', '120.t1.a1', '120.t1.b1', '120.n1.b1', '120.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.x1.e1', '4.x1.h1'], 'contains': ['16.c1.b1', '16.f1.b1', '16.g1.a1', '24.p1.d1', '40.m1.d1'], 'core': '8.m1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 999, 1340, 7531, 2099, 568, 9265], 'generators': [482, 192, 488, 884, 640], 'label': '960.10116.8.m1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.d1', 'normal_contained_in': ['4.e1.a1', '4.x1.h1', '4.x1.e1'], 'normal_contains': ['16.c1.b1', '16.f1.b1', '16.g1.a1', '40.m1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319275
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.x1.a1', '4.x1.f1'], 'contains': ['16.c1.c1', '16.f1.a1', '16.g1.b1', '24.p1.e1', '40.m1.e1'], 'core': '8.m1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 192, 3147, 7531, 2099, 781, 8818], 'generators': [1, 192, 488, 404, 640], 'label': '960.10116.8.m1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.e1', 'normal_contained_in': ['4.e1.b1', '4.x1.a1', '4.x1.f1'], 'normal_contains': ['16.c1.c1', '16.f1.a1', '16.g1.b1', '40.m1.e1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.e1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319276
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.b1', '120.m1.a1', '120.t1.a1', '120.t1.b1', '120.n1.b1', '120.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.x1.b1', '4.x1.e1'], 'contains': ['16.c1.c1', '16.f1.b1', '16.g1.d1', '24.p1.f1', '40.m1.f1'], 'core': '8.m1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 1604, 2503, 7531, 2099, 642, 7650], 'generators': [1, 192, 488, 884, 640], 'label': '960.10116.8.m1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.f1', 'normal_contained_in': ['4.e1.b1', '4.x1.b1', '4.x1.e1'], 'normal_contains': ['16.c1.c1', '16.f1.b1', '16.g1.d1', '40.m1.f1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.f1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319277
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.x1.d1', '4.x1.g1'], 'contains': ['16.c1.d1', '16.f1.a1', '16.g1.d1', '24.p1.g1', '40.m1.g1'], 'core': '8.m1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 2271, 1055, 7531, 2099, 1898, 7416], 'generators': [481, 192, 488, 404, 640], 'label': '960.10116.8.m1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.g1', 'normal_contained_in': ['4.e1.b1', '4.x1.d1', '4.x1.g1'], 'normal_contains': ['16.c1.d1', '16.f1.a1', '16.g1.d1', '40.m1.g1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.g1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319278
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.b1', '120.m1.a1', '120.t1.a1', '120.t1.b1', '120.n1.b1', '120.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '4.x1.c1', '4.x1.h1'], 'contains': ['16.c1.d1', '16.f1.b1', '16.g1.b1', '24.p1.h1', '40.m1.h1'], 'core': '8.m1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [7851, 7095, 375, 549, 7531, 2099, 162, 9942], 'generators': [481, 192, 488, 884, 640], 'label': '960.10116.8.m1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.m1.h1', 'normal_contained_in': ['4.e1.b1', '4.x1.c1', '4.x1.h1'], 'normal_contains': ['16.c1.d1', '16.f1.b1', '16.g1.b1', '40.m1.h1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.h1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.m1.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319279
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': ['120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.x1.a1', '4.x1.b1'], 'contains': ['16.c1.a1', '16.c1.c1', '16.e1.a1', '24.f1.a1', '40.n1.a1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9522, 8777, 656, 1985, 9817, 1344, 295, 7079], 'generators': [1, 640, 192, 2, 488], 'label': '960.10116.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.g1.a1', '4.x1.a1', '4.x1.b1'], 'normal_contains': ['16.c1.a1', '16.c1.c1', '16.e1.a1', '24.f1.a1', '40.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319280
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': ['120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.x1.c1', '4.x1.d1'], 'contains': ['16.c1.a1', '16.c1.d1', '16.e1.b1', '24.f1.b1', '40.n1.b1'], 'core': '8.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9522, 8777, 1182, 680, 9817, 1344, 1563, 8225], 'generators': [481, 640, 192, 2, 488], 'label': '960.10116.8.n1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.b1', 'normal_contained_in': ['4.g1.a1', '4.x1.c1', '4.x1.d1'], 'normal_contains': ['16.c1.d1', '16.c1.a1', '16.e1.b1', '24.f1.b1', '40.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319281
    {'ambient': '960.10116', 'aut_centralizer_order': 12, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '8.c1.a1', 'complements': ['480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.c1.a1', '4.c1.b1', '4.g1.a1', '4.l1.a1', '4.o1.a1', '6.a1.a1', '10.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5321, 7421, 8038, 8666, 6203, 2731, 7426, 1006], 'generators': [1, 488, 240, 640, 2, 480, 192], 'label': '960.10116.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.b1.a1', '4.c1.b1', '4.c1.a1', '4.g1.a1', '4.l1.a1', '4.o1.a1', '6.a1.a1', '10.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319282
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': ['120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.x1.e1', '4.x1.f1'], 'contains': ['16.c1.b1', '16.c1.c1', '16.e1.b1', '24.f1.c1', '40.n1.c1'], 'core': '8.n1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9522, 8777, 1877, 2753, 9817, 1344, 1298, 7298], 'generators': [1, 640, 192, 482, 488], 'label': '960.10116.8.n1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.c1', 'normal_contained_in': ['4.g1.a1', '4.x1.e1', '4.x1.f1'], 'normal_contains': ['16.c1.b1', '16.c1.c1', '16.e1.b1', '24.f1.c1', '40.n1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.n1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319283
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': ['120.t1.a1', '120.t1.b1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.x1.g1', '4.x1.h1'], 'contains': ['16.c1.b1', '16.c1.d1', '16.e1.a1', '24.f1.d1', '40.n1.d1'], 'core': '8.n1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9522, 8777, 2339, 299, 9817, 1344, 1043, 6861], 'generators': [481, 640, 192, 482, 488], 'label': '960.10116.8.n1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.n1.d1', 'normal_contained_in': ['4.g1.a1', '4.x1.g1', '4.x1.h1'], 'normal_contains': ['16.c1.d1', '16.c1.b1', '16.e1.a1', '24.f1.d1', '40.n1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.n1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319284
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.a1', '4.x1.g1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '24.q1.a1', '40.o1.a1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9651, 8079, 2055, 418, 9495, 2321, 1361, 7533], 'generators': [3, 192, 488, 404, 640], 'label': '960.10116.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.i1.a1', '4.x1.g1', '4.x1.a1'], 'normal_contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '40.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319285
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.b1', '120.m1.a1', '120.s1.c1', '120.s1.d1', '120.m1.d1', '120.m1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.c1', '4.x1.e1'], 'contains': ['16.d1.a1', '16.e1.b1', '16.f1.b1', '24.q1.b1', '40.o1.b1'], 'core': '8.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9651, 8079, 1736, 1620, 9495, 2321, 1235, 9041], 'generators': [483, 192, 488, 884, 640], 'label': '960.10116.8.o1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.b1', 'normal_contained_in': ['4.i1.a1', '4.x1.c1', '4.x1.e1'], 'normal_contains': ['16.d1.a1', '16.e1.b1', '16.f1.b1', '40.o1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319286
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.b1', '120.m1.a1', '120.s1.c1', '120.s1.d1', '120.m1.d1', '120.m1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.b1', '4.x1.h1'], 'contains': ['16.d1.b1', '16.e1.a1', '16.f1.b1', '24.q1.c1', '40.o1.c1'], 'core': '8.o1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9651, 8079, 712, 2633, 9495, 2321, 93, 9148], 'generators': [3, 192, 488, 884, 640], 'label': '960.10116.8.o1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.c1', 'normal_contained_in': ['4.i1.a1', '4.x1.h1', '4.x1.b1'], 'normal_contains': ['16.d1.b1', '16.e1.a1', '16.f1.b1', '40.o1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.o1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319287
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.x1.d1', '4.x1.f1'], 'contains': ['16.d1.b1', '16.e1.b1', '16.f1.a1', '24.q1.d1', '40.o1.d1'], 'core': '8.o1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9651, 8079, 1092, 3551, 9495, 2321, 1830, 8935], 'generators': [483, 192, 488, 404, 640], 'label': '960.10116.8.o1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.o1.d1', 'normal_contained_in': ['4.i1.a1', '4.x1.d1', '4.x1.f1'], 'normal_contains': ['16.d1.b1', '16.e1.b1', '16.f1.a1', '40.o1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.o1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319343
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.c1.a1', '6.c1.b1', '6.h1.a1'], 'contains': ['24.e1.a1', '24.g1.a1', '24.h1.a1', '24.n1.a1', '24.n1.b1', '60.m1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3082, -1, 6339, -1, 4231, -1, 5009, -1], 'generators': [731, 480, 192, 4, 8], 'label': '960.10116.12.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '48.51', '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': '2.1'}
  • id: 112319288
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.s1.c1', '120.s1.d1', '120.t1.a1', '120.t1.b1', '120.m1.c1', '120.m1.d1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.a1', '4.x1.h1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.g1.b1', '24.r1.a1', '40.p1.a1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9929, 8393, 26, 801, 9690, 1550, 231, 9714], 'generators': [405, 192, 488, 406, 640], 'label': '960.10116.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.q1.a1', '4.x1.h1', '4.x1.a1'], 'normal_contains': ['16.e1.a1', '16.g1.a1', '16.g1.b1', '40.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319289
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.s1.c1', '120.s1.d1', '120.t1.a1', '120.t1.b1', '120.m1.c1', '120.m1.d1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.b1', '4.x1.g1'], 'contains': ['16.e1.a1', '16.g1.c1', '16.g1.d1', '24.r1.b1', '40.p1.b1'], 'core': '8.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9929, 8393, 2199, 2248, 9690, 1550, 1107, 6970], 'generators': [885, 192, 488, 886, 640], 'label': '960.10116.8.p1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.b1', 'normal_contained_in': ['4.q1.a1', '4.x1.g1', '4.x1.b1'], 'normal_contains': ['16.e1.a1', '16.g1.c1', '16.g1.d1', '40.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319290
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.s1.c1', '120.s1.d1', '120.t1.a1', '120.t1.b1', '120.m1.c1', '120.m1.d1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.d1', '4.x1.e1'], 'contains': ['16.e1.b1', '16.g1.a1', '16.g1.d1', '24.r1.c1', '40.p1.c1'], 'core': '8.p1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9929, 8393, 1820, 1741, 9690, 1550, 1766, 8462], 'generators': [885, 192, 488, 406, 640], 'label': '960.10116.8.p1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.c1', 'normal_contained_in': ['4.q1.a1', '4.x1.d1', '4.x1.e1'], 'normal_contains': ['16.e1.b1', '16.g1.a1', '16.g1.d1', '40.p1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.p1.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319291
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '192.1103', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1', '120.s1.c1', '120.s1.d1', '120.t1.a1', '120.t1.b1', '120.m1.c1', '120.m1.d1', '120.n1.a1', '120.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.x1.c1', '4.x1.f1'], 'contains': ['16.e1.b1', '16.g1.b1', '16.g1.c1', '24.r1.d1', '40.p1.d1'], 'core': '8.p1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9929, 8393, 313, 3015, 9690, 1550, 979, 9494], 'generators': [405, 192, 488, 886, 640], 'label': '960.10116.8.p1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.p1.d1', 'normal_contained_in': ['4.q1.a1', '4.x1.c1', '4.x1.f1'], 'normal_contains': ['16.e1.b1', '16.g1.c1', '16.g1.b1', '40.p1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.p1.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319292
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '24.b1.a1', 'complements': ['480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.d1.b1', '4.f1.a1', '4.f1.b1', '4.g1.a1', '4.p1.a1', '4.r1.a1', '6.g1.a1', '10.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7467, 2805, 4861, 6080, 6891, 7313, 5178, 4882], 'generators': [1, 480, 4, 192, 2, 640, 488], 'label': '960.10116.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.b1', '4.d1.a1', '4.f1.b1', '4.f1.a1', '4.g1.a1', '4.p1.a1', '4.r1.a1', '10.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319293
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.l1.a1', '24.m1.a1', '40.q1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4555, -1, 5757, -1, 439, -1, 3059, -1], 'generators': [2, 192, 8, 4, 640], 'label': '960.10116.8.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.q1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319294
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.b1.b1', '16.i1.a1', '16.l1.a1', '24.m1.b1', '40.q1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4555, -1, 5690, -1, 439, -1, 3197, -1], 'generators': [2, 192, 8, 484, 640], 'label': '960.10116.8.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.q1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319295
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1'], 'contains': ['16.b1.a1', '16.i1.b1', '16.l1.b1', '24.m1.c1', '40.q1.c1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4555, -1, 3580, -1, 439, -1, 2846, -1], 'generators': [1, 192, 8, 4, 640], 'label': '960.10116.8.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.q1.c1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319296
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1'], 'contains': ['16.b1.b1', '16.i1.b1', '16.l1.b1', '24.m1.d1', '40.q1.d1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4555, -1, 3794, -1, 439, -1, 2921, -1], 'generators': [1, 192, 8, 484, 640], 'label': '960.10116.8.q1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.q1.d1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319297
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.k1.a1', '24.n1.a1', '40.r1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1672, -1, 6431, -1, 303, -1, 3265, -1], 'generators': [731, 192, 8, 4, 640], 'label': '960.10116.8.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.r1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319298
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.b1.b1', '16.j1.a1', '16.k1.a1', '24.n1.b1', '40.r1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1672, -1, 6500, -1, 303, -1, 3328, -1], 'generators': [731, 192, 8, 484, 640], 'label': '960.10116.8.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.r1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319299
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.h1.a1', '16.m1.a1', '16.o1.a1', '24.s1.a1', '40.s1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2051, -1, 9250, -1, 179, -1, 9846, -1], 'generators': [2, 640, 192, 240, 480], 'label': '960.10116.8.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.s1.a1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319300
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.h1.b1', '16.m1.a1', '16.o1.a1', '24.s1.b1', '40.s1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2051, -1, 9338, -1, 179, -1, 9783, -1], 'generators': [2, 640, 192, 728, 480], 'label': '960.10116.8.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.s1.b1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319301
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.h1.a1', '16.m1.b1', '16.o1.b1', '24.s1.c1', '40.s1.c1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2051, -1, 9778, -1, 179, -1, 9972, -1], 'generators': [1, 640, 192, 240, 480], 'label': '960.10116.8.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.s1.c1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319302
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '8.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.h1.b1', '16.m1.b1', '16.o1.b1', '24.s1.d1', '40.s1.d1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2051, -1, 9859, -1, 179, -1, 9909, -1], 'generators': [1, 640, 192, 728, 480], 'label': '960.10116.8.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.s1.d1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.s1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319405
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.t1.a1', '8.t1.b1'], 'contains': ['32.c1.a1', '48.p1.a1', '80.p1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [59, -1, 9817, -1, 527, -1, 9347, -1], 'generators': [7, 480, 640, 192], 'label': '960.10116.16.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.p1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319303
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '12.d1.a1', 'complements': ['480.d1.a1', '480.d1.b1', '480.d1.c1', '480.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1', '4.p1.a1', '4.v1.a1', '6.h1.a1', '10.h1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4783, 4535, 7571, 5125, 5666, 7823, 6810, 3845], 'generators': [3, 480, 240, 192, 4, 640, 488], 'label': '960.10116.2.h1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.k1.a1', '4.i1.a1', '4.l1.a1', '4.m1.a1', '4.v1.a1', '4.p1.a1', '10.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319304
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.h1.a1', '16.n1.a1', '16.p1.a1', '24.t1.a1', '40.t1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [215, -1, 9507, -1, 55, -1, 9721, -1], 'generators': [7, 192, 480, 240, 640], 'label': '960.10116.8.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.t1.a1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319305
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '8.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.h1.b1', '16.n1.a1', '16.p1.a1', '24.t1.b1', '40.t1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [215, -1, 9690, -1, 55, -1, 9658, -1], 'generators': [7, 192, 480, 728, 640], 'label': '960.10116.8.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.t1.b1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319306
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['96.d1.c1', '96.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.f1.a1', '20.h1.a1', '20.j1.a1', '20.n1.b1', '20.u1.a1', '30.b1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2904, 918, 6724, 7612, 2512, 6382, 8454, 2099], 'generators': [5, 640, 480, 2, 240, 8], 'label': '960.10116.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '20.b1.a1', '20.f1.a1', '20.h1.a1', '20.j1.a1', '20.n1.b1', '20.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319307
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '5.a1.a1'], 'contains': ['20.a1.b1', '20.b1.b1', '20.f1.b1', '20.h1.a1', '20.j1.b1', '20.n1.a1', '20.u1.b1', '30.b1.b1'], 'core': '10.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2904, 918, 8550, 7490, 2512, 6382, 8389, 2683], 'generators': [1, 640, 480, 6, 240, 488], 'label': '960.10116.10.a1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.b1', 'normal_contained_in': ['2.a1.b1', '5.a1.a1'], 'normal_contains': ['20.a1.b1', '20.b1.b1', '20.f1.b1', '20.h1.a1', '20.j1.b1', '20.n1.a1', '20.u1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.b1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319308
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['96.d1.c1', '96.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.c1.a1', '20.d1.a1', '20.j1.b1', '20.k1.a1', '20.s1.b1', '20.w1.b1', '30.c1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4457, 2460, 7266, 5589, 3072, 8067, 7198, 4649], 'generators': [241, 640, 480, 2, 4, 488], 'label': '960.10116.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '20.c1.a1', '20.d1.a1', '20.j1.b1', '20.k1.a1', '20.s1.b1', '20.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319309
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.a1.b1', '20.c1.b1', '20.d1.b1', '20.j1.a1', '20.k1.a1', '20.s1.a1', '20.w1.a1', '30.c1.b1'], 'core': '10.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4457, 2460, 5778, 4685, 3072, 8067, 6455, 4520], 'generators': [1, 640, 480, 242, 4, 488], 'label': '960.10116.10.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': ['2.b1.b1', '5.a1.a1'], 'normal_contains': ['20.a1.b1', '20.c1.b1', '20.d1.b1', '20.j1.a1', '20.k1.a1', '20.s1.a1', '20.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319310
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': ['96.d1.c1', '96.d1.d1', '96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.d1.a1', '20.e1.a1', '20.m1.a1', '20.n1.a1', '20.s1.a1', '20.t1.a1', '30.d1.a1'], 'core': '10.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6304, 543, 8444, 5750, 3982, 8342, 7739, 4375], 'generators': [2, 640, 480, 4, 240, 8], 'label': '960.10116.10.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1.a1', 'normal_contained_in': ['2.c1.a1', '5.a1.a1'], 'normal_contains': ['20.b1.a1', '20.e1.a1', '20.d1.a1', '20.m1.a1', '20.n1.a1', '20.t1.a1', '20.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319311
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '12.a1.b1', 'complements': ['96.d1.a1', '96.d1.b1', '96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '5.a1.a1'], 'contains': ['20.b1.b1', '20.d1.b1', '20.e1.b1', '20.m1.a1', '20.n1.b1', '20.s1.b1', '20.t1.b1', '30.d1.b1'], 'core': '10.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6304, 543, 6196, 4983, 3982, 8342, 8105, 4215], 'generators': [1, 640, 480, 4, 240, 8], 'label': '960.10116.10.c1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1.b1', 'normal_contained_in': ['2.c1.b1', '5.a1.a1'], 'normal_contains': ['20.b1.b1', '20.e1.b1', '20.d1.b1', '20.m1.a1', '20.n1.b1', '20.t1.b1', '20.s1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.b1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319312
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['96.d1.c1', '96.d1.d1', '96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '20.e1.a1', '20.f1.a1', '20.t1.b1', '20.u1.b1', '20.v1.a1', '20.w1.a1', '30.e1.a1'], 'core': '10.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3868, 2996, 6801, 7138, 3815, 7040, 8190, 1978], 'generators': [241, 640, 480, 2, 404, 488], 'label': '960.10116.10.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.d1.a1', 'normal_contained_in': ['2.d1.a1', '5.a1.a1'], 'normal_contains': ['20.c1.a1', '20.e1.a1', '20.f1.a1', '20.t1.b1', '20.u1.b1', '20.v1.a1', '20.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.d1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319313
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1', '96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '5.a1.a1'], 'contains': ['20.c1.b1', '20.e1.b1', '20.f1.b1', '20.t1.a1', '20.u1.a1', '20.v1.a1', '20.w1.b1', '30.e1.b1'], 'core': '10.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3868, 2996, 7815, 6214, 3815, 7040, 7891, 2804], 'generators': [1, 640, 480, 242, 404, 488], 'label': '960.10116.10.d1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.d1.b1', 'normal_contained_in': ['2.d1.b1', '5.a1.a1'], 'normal_contains': ['20.c1.b1', '20.e1.b1', '20.f1.b1', '20.t1.a1', '20.u1.a1', '20.v1.a1', '20.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.d1.b1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319314
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '24.b1.a1', 'complements': ['480.d1.a1', '480.d1.b1', '480.d1.c1', '480.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.j1.b1', '4.o1.a1', '4.r1.a1', '4.t1.a1', '4.t1.b1', '6.i1.a1', '10.i1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7876, 6141, 5269, 7751, 6362, 5223, 5742, 3574], 'generators': [241, 480, 404, 192, 242, 640, 488], 'label': '960.10116.2.i1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.j1.a1', '4.j1.b1', '4.i1.a1', '4.t1.a1', '4.t1.b1', '4.o1.a1', '4.r1.a1', '10.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319315
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1076197', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.a1.b1', '20.e1.a1', '20.e1.b1', '20.g1.a1', '20.i1.a1', '20.q1.a1', '20.x1.a1', '20.x1.b1', '20.x1.c1', '20.x1.d1', '20.x1.e1', '20.x1.f1', '20.x1.g1', '20.x1.h1', '30.f1.a1'], 'core': '10.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8473, 6150, 4058, 3858, 8219, 3530, 4119, 6008], 'generators': [1, 640, 488, 2, 404, 480], 'label': '960.10116.10.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.e1.a1', 'normal_contained_in': ['2.e1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.b1', '20.a1.a1', '20.e1.b1', '20.e1.a1', '20.g1.a1', '20.i1.a1', '20.q1.a1', '20.x1.c1', '20.x1.d1', '20.x1.g1', '20.x1.h1', '20.x1.a1', '20.x1.b1', '20.x1.e1', '20.x1.f1'], 'normalizer': '1.a1.a1', 'old_label': '10.e1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319316
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '10.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.55643', 'aut_weyl_index': 48, 'centralizer': '8.c1.a1', 'complements': ['96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '5.a1.a1'], 'contains': ['20.b1.a1', '20.b1.b1', '20.c1.a1', '20.c1.b1', '20.g1.a1', '20.l1.a1', '20.o1.a1', '30.a1.a1'], 'core': '10.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 6407, 8844, 8680, 6272, 2622, 8580, 944], 'generators': [1, 480, 488, 2, 240, 640], 'label': '960.10116.10.f1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.f1.a1', 'normal_contained_in': ['2.f1.a1', '5.a1.a1'], 'normal_contains': ['20.b1.b1', '20.b1.a1', '20.c1.b1', '20.c1.a1', '20.g1.a1', '20.l1.a1', '20.o1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.f1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319317
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1076197', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': ['96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '5.a1.a1'], 'contains': ['20.d1.a1', '20.d1.b1', '20.f1.a1', '20.f1.b1', '20.g1.a1', '20.p1.a1', '20.r1.a1', '30.g1.a1'], 'core': '10.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7357, 1176, 5479, 5901, 6795, 8597, 6972, 4769], 'generators': [1, 640, 480, 2, 4, 488], 'label': '960.10116.10.g1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.g1.a1', 'normal_contained_in': ['2.g1.a1', '5.a1.a1'], 'normal_contains': ['20.d1.b1', '20.d1.a1', '20.f1.b1', '20.f1.a1', '20.g1.a1', '20.p1.a1', '20.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.g1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319318
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '10.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20168', 'aut_weyl_index': 32, 'centralizer': '12.d1.a1', 'complements': ['96.d1.a1', '96.d1.b1', '96.d1.c1', '96.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '5.a1.a1'], 'contains': ['20.h1.a1', '20.i1.a1', '20.k1.a1', '20.l1.a1', '20.m1.a1', '20.p1.a1', '20.v1.a1', '30.h1.a1'], 'core': '10.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4766, 3461, 8662, 5273, 5514, 9376, 8258, 3840], 'generators': [3, 640, 480, 4, 240, 488], 'label': '960.10116.10.h1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.h1.a1', 'normal_contained_in': ['2.h1.a1', '5.a1.a1'], 'normal_contains': ['20.h1.a1', '20.k1.a1', '20.i1.a1', '20.l1.a1', '20.m1.a1', '20.v1.a1', '20.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.h1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319319
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1076197', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1', '96.d1.c1', '96.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '5.a1.a1'], 'contains': ['20.i1.a1', '20.j1.a1', '20.j1.b1', '20.o1.a1', '20.r1.a1', '20.t1.a1', '20.t1.b1', '30.i1.a1'], 'core': '10.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8107, 5157, 5577, 7882, 6401, 5512, 7819, 3274], 'generators': [241, 640, 480, 242, 404, 488], 'label': '960.10116.10.i1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.i1.a1', 'normal_contained_in': ['2.i1.a1', '5.a1.a1'], 'normal_contains': ['20.j1.a1', '20.j1.b1', '20.i1.a1', '20.t1.a1', '20.t1.b1', '20.o1.a1', '20.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.i1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319320
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1076197', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1', '96.d1.c1', '96.d1.d1', '96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '5.a1.a1'], 'contains': ['20.l1.a1', '20.n1.a1', '20.n1.b1', '20.q1.a1', '20.r1.a1', '20.w1.a1', '20.w1.b1', '30.j1.a1'], 'core': '10.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7115, 5481, 5636, 8378, 6532, 4851, 7268, 2924], 'generators': [5, 640, 480, 6, 240, 8], 'label': '960.10116.10.j1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.j1.a1', 'normal_contained_in': ['2.j1.a1', '5.a1.a1'], 'normal_contains': ['20.l1.a1', '20.n1.a1', '20.n1.b1', '20.w1.a1', '20.w1.b1', '20.q1.a1', '20.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.j1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319321
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '10.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1076197', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.d1.b1', '96.d1.c1', '96.d1.d1', '96.e1.a1', '96.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '5.a1.a1'], 'contains': ['20.o1.a1', '20.p1.a1', '20.q1.a1', '20.s1.a1', '20.s1.b1', '20.u1.a1', '20.u1.b1', '30.k1.a1'], 'core': '10.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8306, 1686, 8904, 5395, 6664, 6806, 8323, 3950], 'generators': [241, 640, 480, 242, 4, 488], 'label': '960.10116.10.k1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.k1.a1', 'normal_contained_in': ['2.k1.a1', '5.a1.a1'], 'normal_contains': ['20.s1.a1', '20.s1.b1', '20.u1.a1', '20.u1.b1', '20.o1.a1', '20.p1.a1', '20.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.k1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319322
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '24.s1.a1', '24.s1.b1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3438, 6871, 7771, 9790, 4091, 688, 9098, 283], 'generators': [2, 240, 192, 488, 480], 'label': '960.10116.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319323
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1', '6.b1.b1', '6.d1.b1'], 'contains': ['24.a1.b1', '24.b1.a1', '24.d1.b1', '24.s1.c1', '24.s1.d1', '60.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3438, 6871, 7848, 9628, 4091, 688, 9169, 162], 'generators': [1, 240, 192, 488, 480], 'label': '960.10116.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.b1', '24.b1.a1', '24.d1.b1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319324
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.d1.b1', '24.e1.a1', '60.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2324, 8453, 6469, 9313, 4788, 920, 6615, 497], 'generators': [241, 192, 488, 2, 480], 'label': '960.10116.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.d1.b1', '24.e1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319325
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '24.b1.a1', 'complements': ['480.d1.a1', '480.d1.b1', '480.d1.c1', '480.d1.d1', '480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.n1.a1', '4.n1.b1', '4.q1.a1', '4.r1.a1', '4.w1.a1', '4.w1.b1', '6.j1.a1', '10.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7085, 6486, 5439, 8014, 6532, 4851, 5393, 3392], 'generators': [5, 480, 240, 192, 6, 640, 8], 'label': '960.10116.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.n1.a1', '4.n1.b1', '4.w1.a1', '4.w1.b1', '4.q1.a1', '4.r1.a1', '10.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319326
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.a1.a1', '6.c1.b1', '6.e1.b1'], 'contains': ['24.a1.b1', '24.d1.a1', '24.e1.a1', '60.b1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2324, 8453, 7205, 9119, 4788, 920, 6046, 620], 'generators': [1, 192, 488, 242, 480], 'label': '960.10116.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.c1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.b1', '24.d1.a1', '24.e1.a1', '60.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319327
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 96, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.a1.b1', '24.c1.a1', '24.f1.a1', '24.f1.b1', '24.f1.c1', '24.f1.d1', '60.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8681, 9885, 3408, 8294, 9370, 91, 3466, 4445], 'generators': [1, 480, 192, 2, 488], 'label': '960.10116.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.g1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.b1', '24.a1.a1', '24.c1.a1', '24.f1.b1', '24.f1.d1', '24.f1.a1', '24.f1.c1', '60.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319328
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.a1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.e1.a1', '60.d1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5527, 9454, 7576, 9946, 6911, 1139, 6985, 48], 'generators': [3, 192, 488, 240, 480], 'label': '960.10116.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.l1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.e1.a1', '24.c1.a1', '60.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319329
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 96, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.a1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.d1.b1', '60.e1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8842, 8845, 8291, 9499, 8492, 298, 7293, 738], 'generators': [241, 192, 488, 242, 480], 'label': '960.10116.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.o1.a1', '6.a1.a1'], 'normal_contains': ['24.d1.a1', '24.d1.b1', '24.c1.a1', '60.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319330
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '24.j1.b1', '24.o1.a1', '24.o1.b1', '24.o1.c1', '24.o1.d1', '60.f1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2583, -1, 4161, -1, 5647, -1, 3600, -1], 'generators': [405, 480, 192, 2, 488], 'label': '960.10116.12.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319331
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.b1.b1', '6.c1.b1', '6.f1.a1'], 'contains': ['24.a1.b1', '24.g1.a1', '24.j1.a1', '24.o1.e1', '24.o1.f1', '24.o1.g1', '24.o1.h1', '60.f1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2583, -1, 3352, -1, 5647, -1, 2990, -1], 'generators': [1, 480, 192, 406, 488], 'label': '960.10116.12.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.b1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319332
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.k1.a1', '24.m1.a1', '24.m1.b1', '60.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5049, -1, 5810, -1, 4929, -1, 4938, -1], 'generators': [2, 480, 192, 4, 8], 'label': '960.10116.12.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319333
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.c1.b1', '6.d1.b1', '6.g1.a1'], 'contains': ['24.a1.b1', '24.h1.a1', '24.k1.b1', '24.m1.c1', '24.m1.d1', '60.g1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5049, -1, 4500, -1, 4929, -1, 4792, -1], 'generators': [1, 480, 192, 4, 8], 'label': '960.10116.12.g1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319334
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.i1.a1', '24.j1.a1', '24.p1.a1', '24.p1.b1', '24.p1.c1', '24.p1.d1', '60.h1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6868, -1, 4822, -1, 6408, -1, 3533, -1], 'generators': [2, 480, 192, 404, 488], 'label': '960.10116.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319335
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.d1.b1', '6.e1.b1', '6.f1.a1'], 'contains': ['24.a1.b1', '24.i1.a1', '24.j1.b1', '24.p1.e1', '24.p1.f1', '24.p1.g1', '24.p1.h1', '60.h1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6868, -1, 3723, -1, 6408, -1, 3738, -1], 'generators': [1, 480, 192, 404, 488], 'label': '960.10116.12.h1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319336
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '24.b1.a1', 'complements': ['480.d1.a1', '480.d1.b1', '480.d1.c1', '480.d1.d1', '480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.o1.a1', '4.p1.a1', '4.q1.a1', '4.s1.a1', '4.s1.b1', '4.u1.a1', '4.u1.b1', '6.k1.a1', '10.k1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8090, 3310, 7717, 5501, 6703, 5780, 6921, 4006], 'generators': [241, 480, 4, 192, 242, 640, 488], 'label': '960.10116.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.s1.a1', '4.s1.b1', '4.u1.a1', '4.u1.b1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '10.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319337
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.k1.b1', '24.l1.a1', '60.i1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1656, -1, 5127, -1, 4516, -1, 6317, -1], 'generators': [5, 192, 8, 2, 480], 'label': '960.10116.12.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319338
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.b1.b1', '6.e1.b1', '6.g1.a1'], 'contains': ['24.a1.b1', '24.k1.a1', '24.l1.a1', '60.i1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1656, -1, 7056, -1, 4516, -1, 6118, -1], 'generators': [1, 192, 488, 6, 480], 'label': '960.10116.12.i1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319339
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1', '6.b1.b1', '6.h1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.l1.a1', '24.t1.a1', '24.t1.b1', '60.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1015, -1, 7708, -1, 3660, -1, 9028, -1], 'generators': [7, 240, 192, 488, 480], 'label': '960.10116.12.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '24.14', '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': '2.1'}
  • id: 112319340
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.f1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.c1.a1', '24.g1.a1', '24.i1.a1', '24.q1.a1', '24.q1.b1', '24.q1.c1', '24.q1.d1', '60.k1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9100, -1, 3292, -1, 8626, -1, 3667, -1], 'generators': [3, 480, 192, 404, 488], 'label': '960.10116.12.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '48.51', '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': '2.1'}
  • id: 112319341
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.b1.a1', '6.c1.b1', '6.i1.a1'], 'contains': ['24.d1.a1', '24.g1.a1', '24.k1.b1', '60.l1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1925, -1, 4617, -1, 4373, -1, 5757, -1], 'generators': [5, 192, 8, 242, 480], 'label': '960.10116.12.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319342
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.b1.b1', '6.c1.a1', '6.i1.a1'], 'contains': ['24.d1.b1', '24.g1.a1', '24.k1.a1', '60.l1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1925, -1, 6104, -1, 4373, -1, 5974, -1], 'generators': [241, 192, 488, 6, 480], 'label': '960.10116.12.l1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319344
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.d1.a1', '6.d1.b1', '6.h1.a1'], 'contains': ['24.b1.a1', '24.h1.a1', '24.i1.a1', '60.n1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5248, -1, 7454, -1, 5896, -1, 6448, -1], 'generators': [4, 192, 8, 240, 480], 'label': '960.10116.12.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319345
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.b1.b1', '6.d1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.j1.a1', '24.k1.a1', '60.o1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6489, -1, 7144, -1, 5291, -1, 5689, -1], 'generators': [6, 192, 8, 240, 480], 'label': '960.10116.12.o1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319346
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '6.b1.a1', '6.d1.b1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.j1.b1', '24.k1.b1', '60.o1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6489, -1, 4678, -1, 5291, -1, 6385, -1], 'generators': [5, 192, 8, 240, 480], 'label': '960.10116.12.o1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.b1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319347
    {'ambient': '960.10116', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.c1.a1', '6.c1.b1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7226, -1, 5848, -1, 7058, -1, 6119, -1], 'generators': [1, 488, 4, 240, 2, 480, 192], 'label': '960.10116.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '24.14', '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': '4.2'}
  • id: 112319348
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.g1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.h1.a1', '24.l1.a1', '60.p1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7738, -1, 8220, -1, 7036, -1, 6745, -1], 'generators': [3, 192, 488, 4, 480], 'label': '960.10116.12.p1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319349
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.f1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '24.j1.a1', '24.j1.b1', '24.r1.a1', '24.r1.b1', '24.r1.c1', '24.r1.d1', '60.q1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9358, -1, 3208, -1, 9245, -1, 3128, -1], 'generators': [405, 480, 192, 406, 488], 'label': '960.10116.12.q1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319350
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.g1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.c1.a1', '24.k1.a1', '24.k1.b1', '60.r1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7578, -1, 4439, -1, 8760, -1, 5077, -1], 'generators': [5, 192, 8, 6, 480], 'label': '960.10116.12.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319351
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.c1.b1', '6.d1.a1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.h1.a1', '24.j1.a1', '60.s1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6028, -1, 8093, -1, 5772, -1, 5626, -1], 'generators': [242, 192, 8, 4, 480], 'label': '960.10116.12.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319352
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.b1', '6.c1.a1', '6.d1.b1', '6.k1.a1'], 'contains': ['24.d1.b1', '24.h1.a1', '24.j1.b1', '60.s1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6028, -1, 6649, -1, 5772, -1, 6186, -1], 'generators': [241, 192, 8, 4, 480], 'label': '960.10116.12.s1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319353
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.d1.a1', '6.e1.b1', '6.i1.a1'], 'contains': ['24.d1.a1', '24.i1.a1', '24.k1.a1', '60.t1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5808, -1, 6969, -1, 6021, -1, 5825, -1], 'generators': [242, 192, 488, 404, 480], 'label': '960.10116.12.t1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319354
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.b1', '6.d1.b1', '6.e1.a1', '6.i1.a1'], 'contains': ['24.d1.b1', '24.i1.a1', '24.k1.b1', '60.t1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5808, -1, 4978, -1, 6021, -1, 6249, -1], 'generators': [241, 192, 488, 404, 480], 'label': '960.10116.12.t1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319355
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.b1.a1', '6.e1.b1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.j1.b1', '24.l1.a1', '60.u1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1485, -1, 7646, -1, 4652, -1, 7102, -1], 'generators': [405, 192, 488, 242, 480], 'label': '960.10116.12.u1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319356
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.b1', '6.b1.b1', '6.e1.a1', '6.k1.a1'], 'contains': ['24.d1.b1', '24.j1.a1', '24.l1.a1', '60.u1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1485, -1, 8163, -1, 4652, -1, 7927, -1], 'generators': [241, 192, 488, 406, 480], 'label': '960.10116.12.u1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319357
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.e1.a1', '6.e1.b1', '6.h1.a1'], 'contains': ['24.e1.a1', '24.i1.a1', '24.l1.a1', '60.v1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2154, -1, 7278, -1, 5166, -1, 6682, -1], 'generators': [731, 192, 8, 404, 480], 'label': '960.10116.12.v1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319358
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.i1.b1', '8.l1.a1', '8.l1.b1', '8.l1.c1', '8.l1.d1', '12.f1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3014, 4626, 4227, 4319, 3222, 3754, 3661, 6893], 'generators': [405, 640, 480, 192, 2, 488], 'label': '960.10116.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.i1.b1', '8.l1.a1', '8.l1.b1', '8.l1.c1', '8.l1.d1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319359
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.c1.b1', '6.e1.a1', '6.j1.a1'], 'contains': ['24.e1.a1', '24.j1.a1', '24.k1.b1', '60.w1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3637, -1, 4736, -1, 5416, -1, 5354, -1], 'generators': [645, 192, 8, 406, 480], 'label': '960.10116.12.w1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319360
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '6.c1.a1', '6.e1.b1', '6.j1.a1'], 'contains': ['24.e1.a1', '24.j1.b1', '24.k1.a1', '60.w1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3637, -1, 5976, -1, 5416, -1, 5215, -1], 'generators': [725, 192, 488, 6, 480], 'label': '960.10116.12.w1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319361
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '6.f1.a1'], 'contains': ['24.f1.a1', '24.o1.a1', '24.o1.e1', '24.p1.a1', '24.p1.e1', '24.q1.a1', '24.r1.a1', '60.x1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 547, -1, 9943, -1, 2097, -1], 'generators': [1, 404, 192, 2, 488], 'label': '960.10116.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319362
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.b1', '6.f1.a1'], 'contains': ['24.f1.a1', '24.o1.b1', '24.o1.f1', '24.p1.b1', '24.p1.f1', '24.q1.c1', '24.r1.b1', '60.x1.b1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 1424, -1, 9943, -1, 2032, -1], 'generators': [1, 884, 192, 2, 488], 'label': '960.10116.12.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319363
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.c1', '6.f1.a1'], 'contains': ['24.f1.b1', '24.o1.a1', '24.o1.g1', '24.p1.b1', '24.p1.h1', '24.q1.b1', '24.r1.d1', '60.x1.c1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 1343, -1, 9943, -1, 2161, -1], 'generators': [481, 884, 192, 2, 488], 'label': '960.10116.12.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319364
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.d1', '6.f1.a1'], 'contains': ['24.f1.b1', '24.o1.b1', '24.o1.h1', '24.p1.a1', '24.p1.g1', '24.q1.d1', '24.r1.c1', '60.x1.d1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 1721, -1, 9943, -1, 2419, -1], 'generators': [481, 404, 192, 2, 488], 'label': '960.10116.12.x1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319365
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.e1', '6.f1.a1'], 'contains': ['24.f1.c1', '24.o1.c1', '24.o1.e1', '24.p1.d1', '24.p1.f1', '24.q1.b1', '24.r1.c1', '60.x1.e1'], 'core': '24.f1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 2490, -1, 9943, -1, 2290, -1], 'generators': [1, 884, 192, 482, 488], 'label': '960.10116.12.x1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.e1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319366
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.f1', '6.f1.a1'], 'contains': ['24.f1.c1', '24.o1.d1', '24.o1.f1', '24.p1.c1', '24.p1.e1', '24.q1.d1', '24.r1.d1', '60.x1.f1'], 'core': '24.f1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 876, -1, 9943, -1, 2225, -1], 'generators': [1, 404, 192, 482, 488], 'label': '960.10116.12.x1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.f1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319367
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.g1', '6.f1.a1'], 'contains': ['24.f1.d1', '24.o1.c1', '24.o1.g1', '24.p1.c1', '24.p1.g1', '24.q1.a1', '24.r1.b1', '60.x1.g1'], 'core': '24.f1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 2731, -1, 9943, -1, 2354, -1], 'generators': [481, 404, 192, 482, 488], 'label': '960.10116.12.x1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.g1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319368
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '64.196', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.h1', '6.f1.a1'], 'contains': ['24.f1.d1', '24.o1.d1', '24.o1.h1', '24.p1.d1', '24.p1.h1', '24.q1.c1', '24.r1.a1', '60.x1.h1'], 'core': '24.f1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [9638, -1, 808, -1, 9943, -1, 1968, -1], 'generators': [481, 884, 192, 482, 488], 'label': '960.10116.12.x1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.h1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319369
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.a1.b1', '8.b1.a1', '8.i1.a1', '8.l1.e1', '8.l1.f1', '8.l1.g1', '8.l1.h1', '12.f1.b1', '20.a1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3014, 4626, 4047, 3580, 3222, 3754, 3159, 6638], 'generators': [1, 640, 480, 192, 406, 488], 'label': '960.10116.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.b1', '8.b1.a1', '8.i1.a1', '8.l1.g1', '8.l1.h1', '8.l1.e1', '8.l1.f1', '20.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319370
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.10493082', 'aut_weyl_index': 24, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.b1.b1', '30.c1.a1', '30.c1.b1', '30.d1.a1', '30.d1.b1', '30.e1.a1', '30.e1.b1', '30.f1.a1', '30.g1.a1', '30.h1.a1', '30.i1.a1', '30.j1.a1', '30.k1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7283, -1, 7036, -1, 6923, -1, 7962, -1], 'generators': [1, 2, 4, 240], 'label': '960.10116.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319371
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '16.a1', 'aut_quo_index': 10080, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.e1.b1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.i1.b1', '8.j1.a1', '8.j1.b1', '8.k1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.a1', '80.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2823, 4580, 5227, 6704, 2703, 4408, 6063, 3700], 'generators': [488, 640, 192, 480], 'label': '960.10116.16.a1.a1', 'mobius_quo': 2, 'mobius_sub': 64, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.b1', '8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.e1.b1', '8.f1.a1', '8.d1.a1', '8.h1.a1', '8.g1.a1', '8.i1.a1', '8.i1.b1', '8.j1.a1', '8.j1.b1', '8.k1.a1'], 'normal_contains': ['32.c1.a1', '32.a1.a1', '32.b1.a1', '48.a1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319372
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '6.a1.a1', 'complements': ['60.x1.a1', '60.x1.d1', '60.x1.f1', '60.x1.g1', '60.x1.b1', '60.x1.c1', '60.x1.e1', '60.x1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.q1.a1', '8.q1.c1', '8.r1.a1'], 'contains': ['32.a1.a1', '48.h1.a1', '80.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3848, 2442, 5991, 4237, 1827, 8831, 4424, 4129], 'generators': [4, 8, 640, 192], 'label': '960.10116.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.g1.a1'], 'normal_contains': ['32.a1.a1', '80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '96.215', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319373
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '6.a1.a1', 'complements': ['60.x1.b1', '60.x1.c1', '60.x1.e1', '60.x1.h1', '60.x1.a1', '60.x1.d1', '60.x1.f1', '60.x1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.q1.b1', '8.q1.d1', '8.r1.b1'], 'contains': ['32.a1.a1', '48.h1.b1', '80.b1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3848, 2442, 6197, 4359, 1827, 8831, 4488, 4019], 'generators': [484, 8, 640, 192], 'label': '960.10116.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.g1.a1'], 'normal_contains': ['32.a1.a1', '80.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '96.215', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319374
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.l1.a1', '8.l1.b1', '8.m1.a1', '8.m1.b1', '8.n1.a1', '8.n1.b1'], 'contains': ['32.b1.a1', '32.d1.a1', '48.b1.a1', '80.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7638, 8067, 313, 1456, 6872, 2468, 381, 8169], 'generators': [2, 640, 192, 488], 'label': '960.10116.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.l1.a1', '8.l1.b1', '8.m1.b1', '8.m1.a1', '8.n1.b1', '8.n1.a1'], 'normal_contains': ['32.b1.a1', '48.b1.a1', '80.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '96.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319375
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.l1.c1', '8.l1.d1', '8.m1.c1', '8.m1.d1', '8.n1.c1', '8.n1.d1'], 'contains': ['32.b1.a1', '32.d1.b1', '48.b1.b1', '80.c1.b1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7638, 8067, 2060, 2458, 6872, 2468, 508, 7628], 'generators': [482, 640, 192, 488], 'label': '960.10116.16.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.b1', 'normal_contained_in': ['8.a1.a1', '8.l1.c1', '8.l1.d1', '8.m1.d1', '8.m1.c1', '8.n1.d1', '8.n1.c1'], 'normal_contains': ['32.b1.a1', '48.b1.b1', '80.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.b1', 'projective_image': '96.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319490
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.h1.a1', '12.x1.b1', '12.x1.c1'], 'contains': ['48.b1.a1', '48.k1.b1', '48.l1.c1', '120.p1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 815, -1, 7553, -1, 1090, -1], 'generators': [2, 192, 488, 884], 'label': '960.10116.24.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319376
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.l1.e1', '8.l1.f1', '8.m1.e1', '8.m1.f1', '8.n1.a1', '8.n1.c1'], 'contains': ['32.b1.a1', '32.d1.c1', '48.b1.c1', '80.c1.c1'], 'core': '16.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7638, 8067, 1142, 2876, 6872, 2468, 191, 7735], 'generators': [1, 640, 192, 488], 'label': '960.10116.16.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.c1', 'normal_contained_in': ['8.a1.b1', '8.l1.e1', '8.l1.f1', '8.m1.f1', '8.m1.e1', '8.n1.a1', '8.n1.c1'], 'normal_contains': ['32.b1.a1', '48.b1.c1', '80.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.c1', 'projective_image': '96.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319377
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.l1.g1', '8.l1.h1', '8.m1.g1', '8.m1.h1', '8.n1.b1', '8.n1.d1'], 'contains': ['32.b1.a1', '32.d1.d1', '48.b1.d1', '80.c1.d1'], 'core': '16.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7638, 8067, 2244, 416, 6872, 2468, 634, 8062], 'generators': [481, 640, 192, 488], 'label': '960.10116.16.c1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.d1', 'normal_contained_in': ['8.a1.b1', '8.l1.g1', '8.l1.h1', '8.m1.h1', '8.m1.g1', '8.n1.b1', '8.n1.d1'], 'normal_contains': ['32.b1.a1', '48.b1.d1', '80.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.d1', 'projective_image': '96.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319378
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.l1.a1', '8.l1.c1', '8.l1.e1', '8.l1.g1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.b1.a1', '32.e1.a1', '48.j1.a1', '80.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6385, 7240, 2187, 1122, 6748, 3487, 571, 8277], 'generators': [407, 192, 640, 488], 'label': '960.10116.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.l1.g1', '8.l1.a1', '8.l1.c1', '8.l1.e1', '8.o1.b1', '8.o1.a1'], 'normal_contains': ['32.b1.a1', '80.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319379
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.l1.b1', '8.l1.d1', '8.l1.f1', '8.l1.h1', '8.o1.c1', '8.o1.d1'], 'contains': ['32.b1.a1', '32.e1.b1', '48.j1.b1', '80.d1.b1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6385, 7240, 448, 3321, 6748, 3487, 254, 8441], 'generators': [887, 192, 640, 488], 'label': '960.10116.16.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': ['8.b1.a1', '8.l1.h1', '8.l1.b1', '8.l1.d1', '8.l1.f1', '8.o1.d1', '8.o1.c1'], 'normal_contains': ['32.b1.a1', '80.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319380
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['480.d1.c1', '480.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '4.h1.a1', '4.j1.a1', '4.n1.b1', '4.u1.a1', '6.b1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1964, 2468, 5742, 7514, 2264, 5501, 7341, 2286], 'generators': [5, 480, 240, 192, 2, 640, 8], 'label': '960.10116.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '4.h1.a1', '4.j1.a1', '4.n1.b1', '4.u1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '24.14', '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': '24.14'}
  • id: 112319381
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2319', 'aut_weyl_index': 96, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '8.s1.a1', '8.s1.b1', '12.a1.a1', '20.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3280, 1140, 8145, 8872, 1446, 2839, 9026, 829], 'generators': [2, 480, 240, 640, 488, 192], 'label': '960.10116.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.e1.a1', '12.a1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '24.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319382
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '16.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.n1.a1', '8.n1.d1', '8.o1.a1', '8.o1.c1', '8.p1.a1', '8.p1.b1'], 'contains': ['32.b1.a1', '48.c1.a1', '80.e1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9900, 9042, 1923, 1577, 8684, 2311, 142, 7436], 'generators': [3, 192, 488, 640], 'label': '960.10116.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.d1.a1', '8.n1.d1', '8.n1.a1', '8.o1.a1', '8.o1.c1', '8.p1.a1', '8.p1.b1'], 'normal_contains': ['32.b1.a1', '48.c1.a1', '80.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '96.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319383
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '16.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.n1.b1', '8.n1.c1', '8.o1.b1', '8.o1.d1', '8.p1.c1', '8.p1.d1'], 'contains': ['32.b1.a1', '48.c1.b1', '80.e1.b1'], 'core': '16.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9900, 9042, 1199, 2316, 8684, 2311, 746, 8359], 'generators': [483, 192, 488, 640], 'label': '960.10116.16.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': ['8.d1.a1', '8.n1.b1', '8.n1.c1', '8.o1.b1', '8.o1.d1', '8.p1.c1', '8.p1.d1'], 'normal_contains': ['32.b1.a1', '48.c1.b1', '80.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.b1', 'projective_image': '96.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319384
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.m1.a1', '8.m1.c1', '8.m1.e1', '8.m1.g1', '8.o1.a1', '8.o1.d1'], 'contains': ['32.b1.a1', '48.k1.a1', '80.f1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8310, 7812, 1599, 2737, 7300, 3693, 795, 7844], 'generators': [404, 488, 640, 192], 'label': '960.10116.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.h1.a1', '8.m1.g1', '8.m1.a1', '8.m1.c1', '8.m1.e1', '8.o1.a1', '8.o1.d1'], 'normal_contains': ['32.b1.a1', '80.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319385
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.m1.b1', '8.m1.d1', '8.m1.f1', '8.m1.h1', '8.o1.b1', '8.o1.c1'], 'contains': ['32.b1.a1', '48.k1.b1', '80.f1.b1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8310, 7812, 689, 1702, 7300, 3693, 29, 8550], 'generators': [884, 488, 640, 192], 'label': '960.10116.16.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': ['8.h1.a1', '8.m1.h1', '8.m1.b1', '8.m1.d1', '8.m1.f1', '8.o1.b1', '8.o1.c1'], 'normal_contains': ['32.b1.a1', '80.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319386
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.l1.e1', '8.l1.h1', '8.m1.a1', '8.m1.d1', '8.p1.a1', '8.p1.c1'], 'contains': ['32.b1.a1', '48.l1.a1', '80.g1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7268, 7553, 631, 779, 7173, 2789, 317, 8660], 'generators': [406, 488, 640, 192], 'label': '960.10116.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.i1.a1', '8.l1.h1', '8.l1.e1', '8.m1.a1', '8.m1.d1', '8.p1.c1', '8.p1.a1'], 'normal_contains': ['32.b1.a1', '80.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319387
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '8.l1.a1', '8.l1.d1', '8.m1.e1', '8.m1.h1', '8.p1.a1', '8.p1.d1'], 'contains': ['32.b1.a1', '48.l1.b1', '80.g1.b1'], 'core': '16.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7268, 7553, 38, 3024, 7173, 2789, 93, 9384], 'generators': [405, 488, 640, 192], 'label': '960.10116.16.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.b1', 'normal_contained_in': ['8.i1.b1', '8.l1.a1', '8.l1.d1', '8.m1.h1', '8.m1.e1', '8.p1.d1', '8.p1.a1'], 'normal_contains': ['32.b1.a1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319470
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.f1.a1', '12.h1.b1', '12.o1.b1', '12.q1.a1', '12.s1.b1', '12.u1.a1', '12.w1.b1'], 'contains': ['48.a1.a1', '48.l1.b1', '48.l1.d1', '120.j1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6131, -1, 4044, -1, 5963, -1, 5594, -1], 'generators': [405, 192, 488, 480], 'label': '960.10116.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319388
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.l1.f1', '8.l1.g1', '8.m1.b1', '8.m1.c1', '8.p1.b1', '8.p1.d1'], 'contains': ['32.b1.a1', '48.l1.c1', '80.g1.c1'], 'core': '16.g1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7268, 7553, 1540, 2606, 7173, 2789, 444, 7954], 'generators': [886, 488, 640, 192], 'label': '960.10116.16.g1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.c1', 'normal_contained_in': ['8.i1.a1', '8.l1.g1', '8.l1.f1', '8.m1.b1', '8.m1.c1', '8.p1.d1', '8.p1.b1'], 'normal_contains': ['32.b1.a1', '80.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319389
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '8.l1.b1', '8.l1.c1', '8.m1.f1', '8.m1.g1', '8.p1.b1', '8.p1.c1'], 'contains': ['32.b1.a1', '48.l1.d1', '80.g1.d1'], 'core': '16.g1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7268, 7553, 2117, 1851, 7173, 2789, 697, 7519], 'generators': [885, 488, 640, 192], 'label': '960.10116.16.g1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.d1', 'normal_contained_in': ['8.i1.b1', '8.l1.b1', '8.l1.c1', '8.m1.g1', '8.m1.f1', '8.p1.c1', '8.p1.b1'], 'normal_contains': ['32.b1.a1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319390
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '16.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.f1.a1', 'complements': ['60.x1.a1', '60.x1.d1', '60.x1.f1', '60.x1.g1', '60.x1.b1', '60.x1.c1', '60.x1.e1', '60.x1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.s1.a1', '8.s1.c1', '8.t1.a1'], 'contains': ['32.c1.a1', '48.d1.a1', '80.h1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [561, 1127, 9605, 9342, 623, 4251, 9768, 1893], 'generators': [240, 192, 480, 640], 'label': '960.10116.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.c1.a1', '48.d1.a1', '80.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '48.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319391
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '16.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.f1.a1', 'complements': ['60.x1.b1', '60.x1.c1', '60.x1.e1', '60.x1.h1', '60.x1.a1', '60.x1.d1', '60.x1.f1', '60.x1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.s1.b1', '8.s1.d1', '8.t1.b1'], 'contains': ['32.c1.a1', '48.d1.b1', '80.h1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [561, 1127, 9716, 9251, 623, 4251, 9608, 1835], 'generators': [728, 192, 480, 640], 'label': '960.10116.16.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.b1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.c1.a1', '48.d1.b1', '80.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.b1', 'projective_image': '48.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319392
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2319', 'aut_weyl_index': 96, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.f1.a1'], 'contains': ['8.a1.b1', '8.c1.a1', '8.e1.b1', '8.s1.c1', '8.s1.d1', '12.a1.b1', '20.b1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3280, 1140, 8392, 8596, 1446, 2839, 9145, 708], 'generators': [1, 480, 240, 640, 488, 192], 'label': '960.10116.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.f1.a1'], 'normal_contains': ['8.a1.b1', '8.c1.a1', '8.e1.b1', '12.a1.b1', '20.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '24.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319393
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.q1.a1', '8.q1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '48.e1.a1', '80.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3194, -1, 5469, -1, 1599, -1, 4170, -1], 'generators': [2, 640, 192, 8], 'label': '960.10116.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.i1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319394
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.q1.c1', '8.q1.d1'], 'contains': ['32.a1.a1', '32.d1.c1', '32.d1.d1', '48.e1.b1', '80.i1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3194, -1, 3575, -1, 1599, -1, 4107, -1], 'generators': [1, 640, 192, 8], 'label': '960.10116.16.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.i1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319395
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.r1.a1', '8.r1.b1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.e1.b1', '48.f1.a1', '80.j1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [441, -1, 6088, -1, 1407, -1, 4616, -1], 'generators': [407, 192, 640, 8], 'label': '960.10116.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.j1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319396
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.r1.a1', '8.r1.b1'], 'contains': ['32.a1.a1', '48.g1.a1', '80.k1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [717, -1, 6754, -1, 1503, -1, 4853, -1], 'generators': [731, 192, 8, 640], 'label': '960.10116.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.k1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319397
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.q1.a1', '8.q1.b1'], 'contains': ['32.a1.a1', '48.i1.a1', '80.l1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3716, -1, 5552, -1, 1955, -1, 4552, -1], 'generators': [6, 8, 640, 192], 'label': '960.10116.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.l1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319398
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '8.q1.c1', '8.q1.d1'], 'contains': ['32.a1.a1', '48.i1.b1', '80.l1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3716, -1, 3698, -1, 1955, -1, 4296, -1], 'generators': [5, 8, 640, 192], 'label': '960.10116.16.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.l1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319399
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.s1.a1', '8.s1.b1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.d1.b1', '48.m1.a1', '80.m1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1361, -1, 9158, -1, 1283, -1, 8794, -1], 'generators': [2, 640, 192, 480], 'label': '960.10116.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319400
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.s1.c1', '8.s1.d1'], 'contains': ['32.c1.a1', '32.d1.c1', '32.d1.d1', '48.m1.b1', '80.m1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1361, -1, 9760, -1, 1283, -1, 9231, -1], 'generators': [1, 640, 192, 480], 'label': '960.10116.16.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.m1.b1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319401
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 256, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.t1.a1', '8.t1.b1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.e1.b1', '48.n1.a1', '80.n1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [260, -1, 9499, -1, 844, -1, 8730, -1], 'generators': [407, 192, 640, 480], 'label': '960.10116.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.n1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319402
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.s1.a1', '8.s1.b1'], 'contains': ['32.c1.a1', '48.o1.a1', '80.o1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1171, -1, 9351, -1, 939, -1, 9448, -1], 'generators': [242, 192, 480, 640], 'label': '960.10116.16.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.o1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319403
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2319', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.e1.b1', '8.f1.a1', '12.b1.a1', '20.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2467, 5727, 6724, 8449, 2161, 3088, 6823, 1069], 'generators': [241, 480, 640, 192, 2, 488], 'label': '960.10116.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.b1', '8.f1.a1', '12.b1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319404
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '8.s1.c1', '8.s1.d1'], 'contains': ['32.c1.a1', '48.o1.b1', '80.o1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1171, -1, 9898, -1, 939, -1, 9866, -1], 'generators': [241, 192, 480, 640], 'label': '960.10116.16.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.o1.b1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319406
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.e1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.i1.b1', '40.l1.a1', '40.l1.b1', '40.l1.c1', '40.l1.d1', '60.f1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3598, 3652, 4947, 4622, 2997, 5067, 4570, 5856], 'generators': [405, 640, 2, 480, 488], 'label': '960.10116.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.e1.a1'], 'normal_contains': ['40.a1.a1', '40.b1.a1', '40.i1.b1', '40.l1.a1', '40.l1.b1', '40.l1.c1', '40.l1.d1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319407
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '10.a1.b1', '10.b1.b1', '10.e1.a1'], 'contains': ['40.a1.b1', '40.b1.a1', '40.i1.a1', '40.l1.e1', '40.l1.f1', '40.l1.g1', '40.l1.h1', '60.f1.b1'], 'core': '20.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3598, 3652, 4416, 3947, 2997, 5067, 4316, 5497], 'generators': [1, 640, 406, 480, 488], 'label': '960.10116.20.a1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.a1.b1', 'normal_contained_in': ['4.a1.b1', '10.a1.b1', '10.b1.b1', '10.e1.a1'], 'normal_contains': ['40.a1.b1', '40.b1.a1', '40.i1.a1', '40.l1.g1', '40.l1.h1', '40.l1.e1', '40.l1.f1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319408
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '20.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 384, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1', '10.c1.a1', '10.f1.a1'], 'contains': ['40.a1.a1', '40.c1.a1', '40.e1.a1', '40.s1.a1', '40.s1.b1', '60.a1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3296, 388, 9199, 8072, 1445, 3761, 9520, 1189], 'generators': [2, 480, 488, 240, 640], 'label': '960.10116.20.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.b1.a1', '10.a1.a1', '10.c1.a1', '10.f1.a1'], 'normal_contains': ['40.a1.a1', '40.c1.a1', '40.e1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '120.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319409
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '20.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 384, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.a1.b1', '10.c1.b1', '10.f1.a1'], 'contains': ['40.a1.b1', '40.c1.a1', '40.e1.b1', '40.s1.c1', '40.s1.d1', '60.a1.b1'], 'core': '20.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3296, 388, 9262, 8468, 1445, 3761, 9591, 1068], 'generators': [1, 480, 488, 240, 640], 'label': '960.10116.20.b1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.b1.b1', 'normal_contained_in': ['4.b1.b1', '10.a1.b1', '10.c1.b1', '10.f1.a1'], 'normal_contains': ['40.a1.b1', '40.c1.a1', '40.e1.b1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.b1', 'projective_image': '120.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319410
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '20.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 384, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.b1.a1', '10.d1.a1', '10.f1.a1'], 'contains': ['40.a1.a1', '40.e1.b1', '40.f1.a1', '60.b1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4115, 5157, 7461, 8210, 2393, 3993, 8556, 1419], 'generators': [241, 480, 2, 640, 488], 'label': '960.10116.20.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1.a1', 'normal_contained_in': ['4.c1.a1', '10.b1.a1', '10.d1.a1', '10.f1.a1'], 'normal_contains': ['40.a1.a1', '40.e1.b1', '40.f1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319411
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '20.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 384, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '10.b1.b1', '10.d1.b1', '10.f1.a1'], 'contains': ['40.a1.b1', '40.e1.a1', '40.f1.a1', '60.b1.b1'], 'core': '20.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4115, 5157, 8182, 6606, 2393, 3993, 7795, 1651], 'generators': [1, 480, 242, 640, 488], 'label': '960.10116.20.c1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1.b1', 'normal_contained_in': ['4.c1.b1', '10.b1.b1', '10.d1.b1', '10.f1.a1'], 'normal_contains': ['40.a1.b1', '40.e1.a1', '40.f1.a1', '60.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319412
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.b1.a1', '10.c1.a1', '10.g1.a1'], 'contains': ['40.a1.a1', '40.g1.a1', '40.j1.a1', '40.q1.a1', '40.q1.b1', '60.g1.a1'], 'core': '20.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5410, 676, 6799, 5883, 2536, 8512, 5558, 4329], 'generators': [2, 640, 4, 480, 8], 'label': '960.10116.20.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.d1.a1', 'normal_contained_in': ['4.d1.a1', '10.b1.a1', '10.c1.a1', '10.g1.a1'], 'normal_contains': ['40.a1.a1', '40.g1.a1', '40.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319413
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '10.b1.b1', '10.c1.b1', '10.g1.a1'], 'contains': ['40.a1.b1', '40.g1.a1', '40.j1.b1', '40.q1.c1', '40.q1.d1', '60.g1.b1'], 'core': '20.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5410, 676, 5391, 4807, 2536, 8512, 5486, 4205], 'generators': [1, 640, 4, 480, 8], 'label': '960.10116.20.d1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.d1.b1', 'normal_contained_in': ['4.d1.b1', '10.b1.b1', '10.c1.b1', '10.g1.a1'], 'normal_contains': ['40.a1.b1', '40.g1.a1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.d1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319414
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2319', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.d1.b1', '2.f1.a1'], 'contains': ['8.a1.b1', '8.e1.a1', '8.f1.a1', '12.b1.b1', '20.c1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2467, 5727, 7214, 6882, 2161, 3088, 5973, 1210], 'generators': [1, 480, 640, 192, 242, 488], 'label': '960.10116.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.b1.b1', '2.d1.b1', '2.f1.a1'], 'normal_contains': ['8.a1.b1', '8.e1.a1', '8.f1.a1', '12.b1.b1', '20.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319415
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.c1.a1', '10.d1.a1', '10.e1.a1'], 'contains': ['40.a1.a1', '40.h1.a1', '40.i1.a1', '40.m1.a1', '40.m1.b1', '40.m1.c1', '40.m1.d1', '60.h1.a1'], 'core': '20.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6947, 4866, 5140, 5494, 3949, 5289, 4502, 5253], 'generators': [2, 640, 404, 480, 488], 'label': '960.10116.20.e1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.e1.a1', 'normal_contained_in': ['4.e1.a1', '10.c1.a1', '10.d1.a1', '10.e1.a1'], 'normal_contains': ['40.a1.a1', '40.h1.a1', '40.i1.a1', '40.m1.b1', '40.m1.a1', '40.m1.d1', '40.m1.c1'], 'normalizer': '1.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319416
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '10.c1.b1', '10.d1.b1', '10.e1.a1'], 'contains': ['40.a1.b1', '40.h1.a1', '40.i1.b1', '40.m1.e1', '40.m1.f1', '40.m1.g1', '40.m1.h1', '60.h1.b1'], 'core': '20.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6947, 4866, 4490, 4078, 3949, 5289, 4720, 5129], 'generators': [1, 640, 404, 480, 488], 'label': '960.10116.20.e1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.e1.b1', 'normal_contained_in': ['4.e1.b1', '10.c1.b1', '10.d1.b1', '10.e1.a1'], 'normal_contains': ['40.a1.b1', '40.h1.a1', '40.i1.b1', '40.m1.h1', '40.m1.g1', '40.m1.f1', '40.m1.e1'], 'normalizer': '1.a1.a1', 'old_label': '20.e1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319417
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.a1.a1', '10.d1.a1', '10.g1.a1'], 'contains': ['40.a1.a1', '40.j1.b1', '40.k1.a1', '60.i1.a1'], 'core': '20.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2664, 893, 5869, 6967, 2216, 7417, 8373, 2457], 'generators': [5, 640, 2, 8, 480], 'label': '960.10116.20.f1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.f1.a1', 'normal_contained_in': ['4.f1.a1', '10.a1.a1', '10.d1.a1', '10.g1.a1'], 'normal_contains': ['40.a1.a1', '40.j1.b1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.f1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319418
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '10.a1.b1', '10.d1.b1', '10.g1.a1'], 'contains': ['40.a1.b1', '40.j1.a1', '40.k1.a1', '60.i1.b1'], 'core': '20.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2664, 893, 8121, 6476, 2216, 7417, 7672, 3097], 'generators': [1, 640, 6, 488, 480], 'label': '960.10116.20.f1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.f1.b1', 'normal_contained_in': ['4.f1.b1', '10.a1.b1', '10.d1.b1', '10.g1.a1'], 'normal_contains': ['40.a1.b1', '40.j1.a1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.f1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319419
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '20.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '10.e1.a1', '10.f1.a1', '10.g1.a1'], 'contains': ['40.a1.a1', '40.a1.b1', '40.d1.a1', '40.n1.a1', '40.n1.b1', '40.n1.c1', '40.n1.d1', '60.c1.a1'], 'core': '20.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8828, 6679, 4305, 5642, 9003, 2508, 4439, 4901], 'generators': [1, 488, 2, 480, 640], 'label': '960.10116.20.g1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.g1.a1', 'normal_contained_in': ['4.g1.a1', '10.e1.a1', '10.f1.a1', '10.g1.a1'], 'normal_contains': ['40.a1.b1', '40.a1.a1', '40.d1.a1', '40.n1.b1', '40.n1.d1', '40.n1.a1', '40.n1.c1', '60.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.g1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319420
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '20.h1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '10.a1.a1', '10.a1.b1', '10.h1.a1'], 'contains': ['40.b1.a1', '40.c1.a1', '40.k1.a1', '40.t1.a1', '40.t1.b1', '60.j1.a1'], 'core': '20.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2051, 2138, 9117, 7105, 593, 7847, 9444, 2237], 'generators': [7, 640, 488, 240, 480], 'label': '960.10116.20.h1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.h1.a1', 'normal_contained_in': ['4.h1.a1', '10.a1.b1', '10.a1.a1', '10.h1.a1'], 'normal_contains': ['40.b1.a1', '40.c1.a1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.h1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319421
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '20.i1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '10.e1.a1', '10.h1.a1', '10.i1.a1'], 'contains': ['40.b1.a1', '40.d1.a1', '40.h1.a1', '40.o1.a1', '40.o1.b1', '40.o1.c1', '40.o1.d1', '60.k1.a1'], 'core': '20.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8690, 5465, 4245, 4223, 7685, 5537, 4643, 5622], 'generators': [3, 640, 404, 480, 488], 'label': '960.10116.20.i1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.i1.a1', 'normal_contained_in': ['4.i1.a1', '10.e1.a1', '10.h1.a1', '10.i1.a1'], 'normal_contains': ['40.b1.a1', '40.d1.a1', '40.h1.a1', '40.o1.b1', '40.o1.a1', '40.o1.d1', '40.o1.c1'], 'normalizer': '1.a1.a1', 'old_label': '20.i1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319422
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '10.a1.a1', '10.b1.b1', '10.i1.a1'], 'contains': ['40.b1.a1', '40.e1.a1', '40.j1.b1', '60.l1.a1'], 'core': '20.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3435, 2632, 5611, 7311, 2146, 6863, 7408, 3036], 'generators': [5, 640, 242, 8, 480], 'label': '960.10116.20.j1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.j1.a1', 'normal_contained_in': ['4.j1.a1', '10.a1.a1', '10.b1.b1', '10.i1.a1'], 'normal_contains': ['40.b1.a1', '40.e1.a1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.j1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319423
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '10.a1.b1', '10.b1.a1', '10.i1.a1'], 'contains': ['40.b1.a1', '40.e1.b1', '40.j1.a1', '60.l1.b1'], 'core': '20.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3435, 2632, 7097, 7243, 2146, 6863, 7637, 3328], 'generators': [241, 640, 6, 488, 480], 'label': '960.10116.20.j1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.j1.b1', 'normal_contained_in': ['4.j1.b1', '10.a1.b1', '10.b1.a1', '10.i1.a1'], 'normal_contains': ['40.b1.a1', '40.e1.b1', '40.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.j1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.j1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319424
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '20.k1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '10.b1.a1', '10.b1.b1', '10.h1.a1'], 'contains': ['40.b1.a1', '40.f1.a1', '40.g1.a1', '40.r1.a1', '40.r1.b1', '60.m1.a1'], 'core': '20.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3957, 3242, 7340, 4954, 1735, 8970, 5897, 4074], 'generators': [731, 640, 4, 480, 8], 'label': '960.10116.20.k1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.k1.a1', 'normal_contained_in': ['4.k1.a1', '10.b1.b1', '10.b1.a1', '10.h1.a1'], 'normal_contains': ['40.b1.a1', '40.f1.a1', '40.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.k1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319425
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.g1.a1', '8.j1.a1', '8.q1.a1', '8.q1.b1', '12.g1.a1', '20.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4679, 1491, 5980, 5893, 2345, 8869, 4692, 5757], 'generators': [2, 640, 480, 192, 4, 8], 'label': '960.10116.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.g1.a1', '8.j1.a1', '20.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319426
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '20.l1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '32.51', 'aut_weyl_index': 384, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '10.f1.a1', '10.h1.a1', '10.j1.a1'], 'contains': ['40.c1.a1', '40.d1.a1', '40.f1.a1', '60.d1.a1'], 'core': '20.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5090, 6129, 8716, 8596, 6540, 4212, 8802, 953], 'generators': [3, 480, 240, 640, 488], 'label': '960.10116.20.l1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.l1.a1', 'normal_contained_in': ['4.l1.a1', '10.f1.a1', '10.h1.a1', '10.j1.a1'], 'normal_contains': ['40.c1.a1', '40.f1.a1', '40.d1.a1', '60.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.l1.a1', 'projective_image': '120.45', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319427
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '20.m1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '10.c1.a1', '10.c1.b1', '10.h1.a1'], 'contains': ['40.c1.a1', '40.g1.a1', '40.h1.a1', '60.n1.a1'], 'core': '20.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4839, 1095, 8620, 5214, 3398, 9205, 8488, 3730], 'generators': [4, 640, 240, 8, 480], 'label': '960.10116.20.m1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.m1.a1', 'normal_contained_in': ['4.m1.a1', '10.c1.b1', '10.c1.a1', '10.h1.a1'], 'normal_contains': ['40.c1.a1', '40.h1.a1', '40.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.m1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319428
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '10.a1.b1', '10.c1.a1', '10.j1.a1'], 'contains': ['40.c1.a1', '40.i1.a1', '40.j1.a1', '60.o1.a1'], 'core': '20.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6657, 115, 8385, 7639, 2799, 6701, 7358, 2950], 'generators': [6, 640, 240, 8, 480], 'label': '960.10116.20.n1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.n1.a1', 'normal_contained_in': ['4.n1.a1', '10.a1.b1', '10.c1.a1', '10.j1.a1'], 'normal_contains': ['40.c1.a1', '40.i1.a1', '40.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.n1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319429
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.n1.b1', '10.a1.a1', '10.c1.b1', '10.j1.a1'], 'contains': ['40.c1.a1', '40.i1.b1', '40.j1.b1', '60.o1.b1'], 'core': '20.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6657, 115, 5771, 7789, 2799, 6701, 8423, 2604], 'generators': [5, 640, 240, 8, 480], 'label': '960.10116.20.n1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.n1.b1', 'normal_contained_in': ['4.n1.b1', '10.a1.a1', '10.c1.b1', '10.j1.a1'], 'normal_contains': ['40.c1.a1', '40.i1.b1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.n1.b1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319430
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '20.o1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.202', 'aut_weyl_index': 192, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '10.f1.a1', '10.i1.a1', '10.k1.a1'], 'contains': ['40.d1.a1', '40.e1.a1', '40.e1.b1', '60.e1.a1'], 'core': '20.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8421, 6385, 9000, 8340, 7289, 2900, 9273, 1876], 'generators': [241, 480, 242, 640, 488], 'label': '960.10116.20.o1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.o1.a1', 'normal_contained_in': ['4.o1.a1', '10.f1.a1', '10.i1.a1', '10.k1.a1'], 'normal_contains': ['40.e1.a1', '40.e1.b1', '40.d1.a1', '60.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.o1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319431
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '20.p1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '10.g1.a1', '10.h1.a1', '10.k1.a1'], 'contains': ['40.d1.a1', '40.g1.a1', '40.k1.a1', '60.p1.a1'], 'core': '20.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7652, 1587, 8870, 5752, 6666, 8734, 8323, 3620], 'generators': [3, 640, 4, 488, 480], 'label': '960.10116.20.p1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.p1.a1', 'normal_contained_in': ['4.p1.a1', '10.g1.a1', '10.h1.a1', '10.k1.a1'], 'normal_contains': ['40.d1.a1', '40.g1.a1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.p1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319432
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.q1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '10.e1.a1', '10.j1.a1', '10.k1.a1'], 'contains': ['40.d1.a1', '40.i1.a1', '40.i1.b1', '40.p1.a1', '40.p1.b1', '40.p1.c1', '40.p1.d1', '60.q1.a1'], 'core': '20.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8948, 5875, 4359, 4472, 8887, 3339, 4381, 5746], 'generators': [405, 640, 406, 480, 488], 'label': '960.10116.20.q1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.q1.a1', 'normal_contained_in': ['4.q1.a1', '10.e1.a1', '10.j1.a1', '10.k1.a1'], 'normal_contains': ['40.d1.a1', '40.i1.a1', '40.i1.b1', '40.p1.c1', '40.p1.d1', '40.p1.a1', '40.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.q1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319433
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.r1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 64, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '10.g1.a1', '10.i1.a1', '10.j1.a1'], 'contains': ['40.d1.a1', '40.j1.a1', '40.j1.b1', '60.r1.a1'], 'core': '20.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8037, 4568, 5338, 7961, 7810, 6281, 6502, 3398], 'generators': [5, 640, 6, 8, 480], 'label': '960.10116.20.r1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.r1.a1', 'normal_contained_in': ['4.r1.a1', '10.g1.a1', '10.i1.a1', '10.j1.a1'], 'normal_contains': ['40.d1.a1', '40.j1.a1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.r1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319434
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.s1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '10.b1.b1', '10.c1.a1', '10.k1.a1'], 'contains': ['40.e1.a1', '40.g1.a1', '40.i1.a1', '60.s1.a1'], 'core': '20.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6525, 1845, 8773, 5092, 3271, 8082, 7229, 3840], 'generators': [242, 640, 4, 8, 480], 'label': '960.10116.20.s1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.s1.a1', 'normal_contained_in': ['4.s1.a1', '10.b1.b1', '10.c1.a1', '10.k1.a1'], 'normal_contains': ['40.e1.a1', '40.g1.a1', '40.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.s1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319435
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.s1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.b1', '10.b1.a1', '10.c1.b1', '10.k1.a1'], 'contains': ['40.e1.b1', '40.g1.a1', '40.i1.b1', '60.s1.b1'], 'core': '20.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6525, 1845, 7602, 5337, 3271, 8082, 7991, 3950], 'generators': [241, 640, 4, 8, 480], 'label': '960.10116.20.s1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.s1.b1', 'normal_contained_in': ['4.s1.b1', '10.b1.a1', '10.c1.b1', '10.k1.a1'], 'normal_contains': ['40.e1.b1', '40.g1.a1', '40.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.s1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.s1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319436
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.b1', '2.g1.a1'], 'contains': ['8.a1.b1', '8.g1.a1', '8.j1.b1', '8.q1.c1', '8.q1.d1', '12.g1.b1', '20.d1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4679, 1491, 4546, 4865, 2345, 8869, 4588, 5579], 'generators': [1, 640, 480, 192, 4, 8], 'label': '960.10116.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.b1.b1', '2.c1.b1', '2.g1.a1'], 'normal_contains': ['8.a1.b1', '8.g1.a1', '8.j1.b1', '20.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319437
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.t1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '10.c1.a1', '10.d1.b1', '10.i1.a1'], 'contains': ['40.e1.a1', '40.h1.a1', '40.j1.a1', '60.t1.a1'], 'core': '20.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6002, 2950, 8244, 6737, 3526, 7255, 7458, 3243], 'generators': [242, 640, 404, 488, 480], 'label': '960.10116.20.t1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.t1.a1', 'normal_contained_in': ['4.t1.a1', '10.c1.a1', '10.d1.b1', '10.i1.a1'], 'normal_contains': ['40.e1.a1', '40.h1.a1', '40.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.t1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319438
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.t1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.b1', '10.c1.b1', '10.d1.a1', '10.i1.a1'], 'contains': ['40.e1.b1', '40.h1.a1', '40.j1.b1', '60.t1.b1'], 'core': '20.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6002, 2950, 5701, 7407, 3526, 7255, 8055, 2841], 'generators': [241, 640, 404, 488, 480], 'label': '960.10116.20.t1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.t1.b1', 'normal_contained_in': ['4.t1.b1', '10.c1.b1', '10.d1.a1', '10.i1.a1'], 'normal_contains': ['40.e1.b1', '40.h1.a1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.t1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.t1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319439
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.u1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '10.a1.a1', '10.d1.b1', '10.k1.a1'], 'contains': ['40.e1.a1', '40.i1.b1', '40.k1.a1', '60.u1.a1'], 'core': '20.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2591, 2431, 8496, 6230, 2286, 6978, 9223, 2397], 'generators': [405, 640, 242, 488, 480], 'label': '960.10116.20.u1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.u1.a1', 'normal_contained_in': ['4.u1.a1', '10.a1.a1', '10.d1.b1', '10.k1.a1'], 'normal_contains': ['40.e1.a1', '40.i1.b1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.u1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.u1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319440
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.u1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.b1', '10.a1.b1', '10.d1.a1', '10.k1.a1'], 'contains': ['40.e1.b1', '40.i1.a1', '40.k1.a1', '60.u1.b1'], 'core': '20.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2591, 2431, 8954, 6832, 2286, 6978, 9323, 2336], 'generators': [241, 640, 406, 488, 480], 'label': '960.10116.20.u1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.u1.b1', 'normal_contained_in': ['4.u1.b1', '10.a1.b1', '10.d1.a1', '10.k1.a1'], 'normal_contains': ['40.e1.b1', '40.i1.a1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.u1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.u1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319441
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '20.v1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '10.d1.a1', '10.d1.b1', '10.h1.a1'], 'contains': ['40.f1.a1', '40.h1.a1', '40.k1.a1', '60.v1.a1'], 'core': '20.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3067, 4170, 8315, 6381, 2672, 8290, 8625, 2113], 'generators': [731, 640, 404, 8, 480], 'label': '960.10116.20.v1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.v1.a1', 'normal_contained_in': ['4.v1.a1', '10.d1.b1', '10.d1.a1', '10.h1.a1'], 'normal_contains': ['40.f1.a1', '40.h1.a1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.v1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319442
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.w1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '10.b1.b1', '10.d1.a1', '10.j1.a1'], 'contains': ['40.f1.a1', '40.i1.a1', '40.j1.b1', '60.w1.a1'], 'core': '20.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4406, 3853, 5656, 7884, 2898, 7093, 6830, 2518], 'generators': [5, 640, 406, 8, 480], 'label': '960.10116.20.w1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.w1.a1', 'normal_contained_in': ['4.w1.a1', '10.b1.b1', '10.d1.a1', '10.j1.a1'], 'normal_contains': ['40.f1.a1', '40.i1.a1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.w1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.w1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319443
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '20.w1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '10.b1.a1', '10.d1.b1', '10.j1.a1'], 'contains': ['40.f1.a1', '40.i1.b1', '40.j1.a1', '60.w1.b1'], 'core': '20.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4406, 3853, 7129, 6899, 2898, 7093, 6795, 3157], 'generators': [405, 640, 6, 488, 480], 'label': '960.10116.20.w1.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.w1.b1', 'normal_contained_in': ['4.w1.b1', '10.b1.a1', '10.d1.b1', '10.j1.a1'], 'normal_contains': ['40.f1.a1', '40.i1.b1', '40.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.w1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.w1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319444
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.a1', '48.h1.b1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '10.e1.a1'], 'contains': ['40.l1.a1', '40.l1.e1', '40.m1.a1', '40.m1.e1', '40.n1.a1', '40.o1.a1', '40.p1.a1', '60.x1.a1'], 'core': '20.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 2438, 958, 9591, 1712, 2613, 6595], 'generators': [1, 640, 2, 404, 488], 'label': '960.10116.20.x1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.a1', 'normal_contained_in': ['4.x1.a1', '10.e1.a1'], 'normal_contains': ['40.l1.a1', '40.l1.e1', '40.m1.a1', '40.m1.e1', '40.n1.a1', '40.o1.a1', '40.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.a1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319445
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.b1', '48.h1.a1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.b1', '10.e1.a1'], 'contains': ['40.l1.b1', '40.l1.f1', '40.m1.b1', '40.m1.f1', '40.n1.a1', '40.o1.c1', '40.p1.b1', '60.x1.b1'], 'core': '20.x1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 2725, 2622, 9591, 1712, 2578, 6413], 'generators': [1, 640, 2, 884, 488], 'label': '960.10116.20.x1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.b1', 'normal_contained_in': ['4.x1.b1', '10.e1.a1'], 'normal_contains': ['40.l1.b1', '40.l1.f1', '40.m1.b1', '40.m1.f1', '40.n1.a1', '40.o1.c1', '40.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.b1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319446
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.b1', '48.h1.a1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.c1', '10.e1.a1'], 'contains': ['40.l1.a1', '40.l1.g1', '40.m1.b1', '40.m1.h1', '40.n1.b1', '40.o1.b1', '40.p1.d1', '60.x1.c1'], 'core': '20.x1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 2587, 457, 9591, 1712, 2649, 6716], 'generators': [481, 640, 2, 884, 488], 'label': '960.10116.20.x1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.c1', 'normal_contained_in': ['4.x1.c1', '10.e1.a1'], 'normal_contains': ['40.l1.g1', '40.l1.a1', '40.m1.h1', '40.m1.b1', '40.n1.b1', '40.o1.b1', '40.p1.d1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.c1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319447
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.h1.a1', '8.i1.a1', '8.m1.a1', '8.m1.b1', '8.m1.c1', '8.m1.d1', '12.h1.a1', '20.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6024, 5352, 5304, 4494, 4177, 4042, 3387, 6329], 'generators': [2, 640, 480, 192, 404, 488], 'label': '960.10116.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.h1.a1', '8.i1.a1', '8.m1.b1', '8.m1.a1', '8.m1.d1', '8.m1.c1', '20.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '48.51', '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': '12.4'}
  • id: 112319448
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.a1', '48.h1.b1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.d1', '10.e1.a1'], 'contains': ['40.l1.b1', '40.l1.h1', '40.m1.a1', '40.m1.g1', '40.n1.b1', '40.o1.d1', '40.p1.c1', '60.x1.d1'], 'core': '20.x1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 2770, 1491, 9591, 1712, 2791, 6534], 'generators': [481, 640, 2, 404, 488], 'label': '960.10116.20.x1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.d1', 'normal_contained_in': ['4.x1.d1', '10.e1.a1'], 'normal_contains': ['40.l1.h1', '40.l1.b1', '40.m1.g1', '40.m1.a1', '40.n1.b1', '40.o1.d1', '40.p1.c1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.d1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319449
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.b1', '48.h1.a1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.e1', '10.e1.a1'], 'contains': ['40.l1.c1', '40.l1.e1', '40.m1.d1', '40.m1.f1', '40.n1.c1', '40.o1.b1', '40.p1.c1', '60.x1.e1'], 'core': '20.x1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 3087, 1681, 9591, 1712, 2720, 6474], 'generators': [1, 640, 482, 884, 488], 'label': '960.10116.20.x1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.e1', 'normal_contained_in': ['4.x1.e1', '10.e1.a1'], 'normal_contains': ['40.l1.c1', '40.l1.e1', '40.m1.d1', '40.m1.f1', '40.n1.c1', '40.o1.b1', '40.p1.c1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.e1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319450
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.a1', '48.h1.b1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.f1', '10.e1.a1'], 'contains': ['40.l1.d1', '40.l1.f1', '40.m1.c1', '40.m1.e1', '40.n1.c1', '40.o1.d1', '40.p1.d1', '60.x1.f1'], 'core': '20.x1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 2542, 3686, 9591, 1712, 2684, 6656], 'generators': [1, 640, 482, 404, 488], 'label': '960.10116.20.x1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.f1', 'normal_contained_in': ['4.x1.f1', '10.e1.a1'], 'normal_contains': ['40.l1.d1', '40.l1.f1', '40.m1.c1', '40.m1.e1', '40.n1.c1', '40.o1.d1', '40.p1.d1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.f1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319451
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.a1', '48.h1.b1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.g1', '10.e1.a1'], 'contains': ['40.l1.c1', '40.l1.g1', '40.m1.c1', '40.m1.g1', '40.n1.d1', '40.o1.a1', '40.p1.b1', '60.x1.g1'], 'core': '20.x1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 3209, 735, 9591, 1712, 2755, 6353], 'generators': [481, 640, 482, 404, 488], 'label': '960.10116.20.x1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.g1', 'normal_contained_in': ['4.x1.g1', '10.e1.a1'], 'normal_contains': ['40.l1.g1', '40.l1.c1', '40.m1.g1', '40.m1.c1', '40.n1.d1', '40.o1.a1', '40.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.g1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319452
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '20.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '96.209', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1', '48.h1.b1', '48.h1.a1', '48.o1.a1', '48.i1.a1', '48.o1.b1', '48.i1.b1', '48.g1.a1', '48.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.h1', '10.e1.a1'], 'contains': ['40.l1.d1', '40.l1.h1', '40.m1.d1', '40.m1.h1', '40.n1.d1', '40.o1.c1', '40.p1.a1', '60.x1.h1'], 'core': '20.x1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [9562, 7799, 2483, 1423, 9591, 1712, 2542, 6776], 'generators': [481, 640, 482, 884, 488], 'label': '960.10116.20.x1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.x1.h1', 'normal_contained_in': ['4.x1.h1', '10.e1.a1'], 'normal_contains': ['40.l1.h1', '40.l1.d1', '40.m1.h1', '40.m1.d1', '40.n1.d1', '40.o1.c1', '40.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.x1.h1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.x1.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319453
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.e1.a1', '48.m1.a1', '120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2737, 7056, 5019, 8892, 4833, 920, 5662, 3276], 'generators': [2, 480, 192, 488], 'label': '960.10116.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319454
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.a1.b1', '12.b1.b1', '12.c1.a1', '12.f1.b1', '12.g1.b1', '12.h1.b1', '12.i1.b1'], 'contains': ['48.a1.a1', '48.b1.c1', '48.b1.d1', '48.e1.b1', '48.m1.b1', '120.a1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2737, 7056, 3836, 8730, 4833, 920, 5527, 3044], 'generators': [1, 480, 192, 488], 'label': '960.10116.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['8.a1.b1', '12.a1.b1', '12.b1.b1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.d1', '48.b1.c1', '120.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319455
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '24.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.a1.b1', '12.d1.a1', '12.j1.a1', '12.n1.a1', '12.o1.a1', '12.o1.b1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.d1.b1', '120.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3856, 6316, 7817, 9897, 4072, 1780, 8285, 888], 'generators': [488, 192, 480, 240], 'label': '960.10116.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.b1', '12.a1.a1', '12.d1.a1'], 'normal_contains': ['48.a1.a1', '48.d1.b1', '48.d1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '24.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319456
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.k1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.c1.b1', '120.c1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9162, 9299, 3517, 9021, 8153, 588, 5389, 2929], 'generators': [3, 192, 488, 480], 'label': '960.10116.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.d1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.b1', '48.c1.a1', '120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319457
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '24.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.a1.a1', '12.b1.b1', '12.e1.a1', '12.l1.a1', '12.s1.a1', '12.t1.a1', '12.u1.a1'], 'contains': ['48.a1.a1', '48.o1.a1', '120.d1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2239, 8209, 7957, 9666, 4337, 1137, 7354, 1692], 'generators': [242, 192, 480, 488], 'label': '960.10116.24.d1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.e1.a1', '12.a1.a1', '12.b1.b1', '12.e1.a1'], 'normal_contains': ['48.a1.a1', '120.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319458
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '2.d1.b1', '2.e1.a1'], 'contains': ['8.a1.b1', '8.h1.a1', '8.i1.b1', '8.m1.e1', '8.m1.f1', '8.m1.g1', '8.m1.h1', '12.h1.b1', '20.e1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6024, 5352, 4143, 3749, 4177, 4042, 3903, 6152], 'generators': [1, 640, 480, 192, 404, 488], 'label': '960.10116.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.c1.b1', '2.d1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.b1', '8.h1.a1', '8.i1.b1', '8.m1.h1', '8.m1.g1', '8.m1.f1', '8.m1.e1', '20.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '48.51', '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': '12.4'}
  • id: 112319459
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '24.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.a1.b1', '12.b1.a1', '12.e1.a1', '12.l1.b1', '12.s1.b1', '12.t1.b1', '12.u1.b1'], 'contains': ['48.a1.a1', '48.o1.b1', '120.d1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2239, 8209, 7296, 9546, 4337, 1137, 7814, 1510], 'generators': [241, 192, 480, 488], 'label': '960.10116.24.d1.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.d1.b1', 'normal_contained_in': ['8.e1.b1', '12.a1.b1', '12.b1.a1', '12.e1.a1'], 'normal_contains': ['48.a1.a1', '120.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319460
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '24.e1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.b1.a1', '12.b1.b1', '12.d1.a1', '12.m1.a1', '12.v1.a1', '12.w1.a1', '12.w1.b1'], 'contains': ['48.a1.a1', '48.g1.a1', '120.e1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1869, 8640, 6733, 9399, 4461, 1983, 6874, 1299], 'generators': [731, 192, 8, 480], 'label': '960.10116.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.f1.a1', '12.b1.b1', '12.b1.a1', '12.d1.a1'], 'normal_contains': ['48.a1.a1', '120.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319461
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '4.m1.a1', 'complements': ['40.t1.a1', '40.t1.b1', '40.r1.a1', '40.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.c1.a1', '12.x1.a1', '12.x1.b1'], 'contains': ['48.b1.a1', '48.b1.c1', '48.c1.a1', '120.f1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9673, 9710, 515, 4335, 9303, 231, 1033, 4856], 'generators': [1, 192, 488, 2], 'label': '960.10116.24.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': ['8.n1.a1', '12.c1.a1'], 'normal_contains': ['48.b1.a1', '48.b1.c1', '48.c1.a1', '120.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319462
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '4.m1.a1', 'complements': ['40.t1.a1', '40.t1.b1', '40.r1.a1', '40.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '12.c1.a1', '12.x1.c1', '12.x1.d1'], 'contains': ['48.b1.a1', '48.b1.d1', '48.c1.b1', '120.f1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9673, 9710, 1030, 3660, 9303, 231, 2107, 5036], 'generators': [481, 192, 488, 2], 'label': '960.10116.24.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': ['8.n1.b1', '12.c1.a1'], 'normal_contains': ['48.b1.d1', '48.b1.a1', '48.c1.b1', '120.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319463
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '4.m1.a1', 'complements': ['40.t1.a1', '40.t1.b1', '40.r1.a1', '40.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.c1', '12.c1.a1', '12.x1.e1', '12.x1.f1'], 'contains': ['48.b1.b1', '48.b1.c1', '48.c1.b1', '120.f1.c1'], 'core': '24.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9673, 9710, 1659, 4464, 9303, 231, 1875, 4946], 'generators': [1, 192, 488, 482], 'label': '960.10116.24.f1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.c1', 'normal_contained_in': ['8.n1.c1', '12.c1.a1'], 'normal_contains': ['48.b1.b1', '48.b1.c1', '48.c1.b1', '120.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319464
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '4.m1.a1', 'complements': ['40.t1.a1', '40.t1.b1', '40.r1.a1', '40.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.d1', '12.c1.a1', '12.x1.g1', '12.x1.h1'], 'contains': ['48.b1.b1', '48.b1.d1', '48.c1.a1', '120.f1.d1'], 'core': '24.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9673, 9710, 2903, 3872, 9303, 231, 1654, 4766], 'generators': [481, 192, 488, 482], 'label': '960.10116.24.f1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.d1', 'normal_contained_in': ['8.n1.d1', '12.c1.a1'], 'normal_contains': ['48.b1.d1', '48.b1.b1', '48.c1.a1', '120.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.2', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319465
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.f1.a1', '12.f1.b1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.l1.b1', '12.m1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.j1.a1', '48.j1.b1', '48.n1.a1', '120.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1230, -1, 4697, -1, 4205, -1, 5456, -1], 'generators': [407, 480, 192, 488], 'label': '960.10116.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '48.51', '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': '2.1'}
  • id: 112319466
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.g1.a1', '12.g1.b1', '12.m1.a1', '12.n1.a1', '12.p1.a1', '12.s1.a1', '12.s1.b1'], 'contains': ['48.a1.a1', '48.h1.a1', '48.h1.b1', '120.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5264, -1, 6921, -1, 4966, -1, 6685, -1], 'generators': [4, 192, 8, 480], 'label': '960.10116.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '48.51', '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': '1.1'}
  • id: 112319467
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.h1.a1', '12.h1.b1', '12.k1.a1', '12.n1.a1', '12.t1.a1', '12.t1.b1', '12.v1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.k1.b1', '120.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5821, -1, 4827, -1, 6213, -1, 5729, -1], 'generators': [404, 192, 488, 480], 'label': '960.10116.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319468
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.f1.b1', '12.h1.a1', '12.o1.a1', '12.q1.a1', '12.s1.a1', '12.u1.b1', '12.w1.a1'], 'contains': ['48.a1.a1', '48.l1.a1', '48.l1.c1', '120.j1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6131, -1, 4758, -1, 5963, -1, 5222, -1], 'generators': [406, 192, 488, 480], 'label': '960.10116.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319469
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.j1.b1', '8.k1.a1', '12.i1.a1', '20.f1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1964, 2498, 5588, 7173, 1888, 6590, 6600, 2209], 'generators': [5, 640, 192, 8, 2, 480], 'label': '960.10116.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.j1.b1', '8.k1.a1', '20.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319471
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.g1.a1', '12.i1.b1', '12.l1.b1', '12.o1.a1', '12.r1.a1', '12.t1.a1', '12.w1.b1'], 'contains': ['48.a1.a1', '48.i1.a1', '120.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4586, -1, 6216, -1, 5090, -1, 6748, -1], 'generators': [6, 192, 8, 480], 'label': '960.10116.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.k1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319472
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '12.g1.b1', '12.i1.a1', '12.l1.a1', '12.o1.b1', '12.r1.a1', '12.t1.b1', '12.w1.a1'], 'contains': ['48.a1.a1', '48.i1.b1', '120.k1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4586, -1, 3988, -1, 5090, -1, 6811, -1], 'generators': [5, 192, 8, 480], 'label': '960.10116.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.k1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319473
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.i1.a1', '12.i1.b1', '12.j1.a1', '12.p1.a1', '12.u1.a1', '12.u1.b1', '12.v1.a1'], 'contains': ['48.a1.a1', '48.p1.a1', '120.l1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [912, -1, 7874, -1, 3948, -1, 7877, -1], 'generators': [7, 192, 480, 488], 'label': '960.10116.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319474
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.g1.a1'], 'contains': ['48.e1.a1', '48.h1.a1', '48.i1.a1', '120.m1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4806, -1, 5948, -1, 3450, -1, 4679, -1], 'generators': [2, 192, 8, 4], 'label': '960.10116.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.m1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319475
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.g1.a1'], 'contains': ['48.e1.a1', '48.h1.b1', '48.i1.a1', '120.m1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4806, -1, 5892, -1, 3450, -1, 4742, -1], 'generators': [2, 192, 8, 484], 'label': '960.10116.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.m1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319476
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.c1', '12.g1.b1'], 'contains': ['48.e1.b1', '48.h1.a1', '48.i1.b1', '120.m1.c1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4806, -1, 3640, -1, 3450, -1, 4233, -1], 'generators': [1, 192, 8, 4], 'label': '960.10116.24.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.m1.c1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319477
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.d1', '12.g1.b1'], 'contains': ['48.e1.b1', '48.h1.b1', '48.i1.b1', '120.m1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4806, -1, 3722, -1, 3450, -1, 4360, -1], 'generators': [1, 192, 8, 484], 'label': '960.10116.24.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.m1.d1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319478
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '12.m1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.h1.a1', '120.n1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1398, -1, 6581, -1, 2207, -1, 4805, -1], 'generators': [731, 192, 8, 4], 'label': '960.10116.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.n1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319479
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.b1', '12.m1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.h1.b1', '120.n1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1398, -1, 6637, -1, 2207, -1, 4902, -1], 'generators': [731, 192, 8, 484], 'label': '960.10116.24.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.n1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319480
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.d1.b1', '2.g1.a1'], 'contains': ['8.a1.b1', '8.j1.a1', '8.k1.a1', '12.i1.b1', '20.f1.b1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1964, 2498, 7067, 6478, 1888, 6590, 6047, 3386], 'generators': [1, 640, 192, 488, 6, 480], 'label': '960.10116.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.a1.b1', '2.d1.b1', '2.g1.a1'], 'normal_contains': ['8.a1.b1', '8.j1.a1', '8.k1.a1', '20.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319481
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.f1.a1', '12.x1.a1', '12.x1.c1'], 'contains': ['48.b1.a1', '48.j1.a1', '48.l1.b1', '120.o1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 179, -1, 7057, -1, 1380, -1], 'generators': [405, 192, 488, 2], 'label': '960.10116.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319482
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '12.f1.a1', '12.x1.b1', '12.x1.d1'], 'contains': ['48.b1.a1', '48.j1.b1', '48.l1.d1', '120.o1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 1108, -1, 7057, -1, 1760, -1], 'generators': [885, 192, 488, 2], 'label': '960.10116.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319483
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.c1', '12.f1.a1', '12.x1.e1', '12.x1.g1'], 'contains': ['48.b1.b1', '48.j1.a1', '48.l1.d1', '120.o1.c1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 1995, -1, 7057, -1, 2222, -1], 'generators': [885, 192, 488, 482], 'label': '960.10116.24.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319484
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.d1', '12.f1.a1', '12.x1.f1', '12.x1.h1'], 'contains': ['48.b1.b1', '48.j1.b1', '48.l1.b1', '120.o1.d1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 305, -1, 7057, -1, 1148, -1], 'generators': [405, 192, 488, 482], 'label': '960.10116.24.o1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319485
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.e1', '12.f1.b1', '12.x1.a1', '12.x1.e1'], 'contains': ['48.b1.c1', '48.j1.a1', '48.l1.a1', '120.o1.e1'], 'core': '48.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 1612, -1, 7057, -1, 1495, -1], 'generators': [1, 192, 488, 406], 'label': '960.10116.24.o1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.e1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319486
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.f1', '12.f1.b1', '12.x1.b1', '12.x1.f1'], 'contains': ['48.b1.c1', '48.j1.b1', '48.l1.c1', '120.o1.f1'], 'core': '48.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 680, -1, 7057, -1, 1201, -1], 'generators': [1, 192, 488, 886], 'label': '960.10116.24.o1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.f1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319487
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.g1', '12.f1.b1', '12.x1.c1', '12.x1.g1'], 'contains': ['48.b1.d1', '48.j1.a1', '48.l1.c1', '120.o1.g1'], 'core': '48.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 2964, -1, 7057, -1, 2054, -1], 'generators': [481, 192, 488, 886], 'label': '960.10116.24.o1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.g1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319488
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.h1', '12.f1.b1', '12.x1.d1', '12.x1.h1'], 'contains': ['48.b1.d1', '48.j1.b1', '48.l1.a1', '120.o1.h1'], 'core': '48.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 619, -1, 7057, -1, 1548, -1], 'generators': [481, 192, 488, 406], 'label': '960.10116.24.o1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.h1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319489
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.h1.a1', '12.x1.a1', '12.x1.d1'], 'contains': ['48.b1.a1', '48.k1.a1', '48.l1.a1', '120.p1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 231, -1, 7553, -1, 1996, -1], 'generators': [2, 192, 488, 404], 'label': '960.10116.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319491
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['480.d1.a1', '480.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.b1.b1', '4.f1.b1', '4.h1.a1', '4.j1.b1', '4.n1.a1', '4.u1.b1', '6.b1.b1', '10.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1964, 2468, 7483, 7371, 2264, 5501, 7233, 3043], 'generators': [1, 480, 240, 192, 6, 640, 488], 'label': '960.10116.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.b1.b1', '4.f1.b1', '4.h1.a1', '4.j1.b1', '4.n1.a1', '4.u1.b1', '10.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '24.14', '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': '24.14'}
  • id: 112319492
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.27015', 'aut_weyl_index': 48, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.d1.a1', '8.n1.a1', '8.n1.b1', '8.n1.c1', '8.n1.d1', '12.c1.a1', '20.g1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8249, 8281, 3119, 5478, 8492, 1934, 3303, 5899], 'generators': [1, 488, 480, 640, 2, 192], 'label': '960.10116.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.b1', '8.a1.a1', '8.d1.a1', '8.n1.b1', '8.n1.d1', '8.n1.a1', '8.n1.c1', '12.c1.a1', '20.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319493
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.c1', '12.h1.a1', '12.x1.f1', '12.x1.g1'], 'contains': ['48.b1.b1', '48.k1.a1', '48.l1.c1', '120.p1.c1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 1711, -1, 7553, -1, 2164, -1], 'generators': [482, 192, 488, 404], 'label': '960.10116.24.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319494
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.d1', '12.h1.a1', '12.x1.e1', '12.x1.h1'], 'contains': ['48.b1.b1', '48.k1.b1', '48.l1.a1', '120.p1.d1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 732, -1, 7553, -1, 1259, -1], 'generators': [482, 192, 488, 884], 'label': '960.10116.24.p1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319495
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.e1', '12.h1.b1', '12.x1.a1', '12.x1.f1'], 'contains': ['48.b1.c1', '48.k1.a1', '48.l1.b1', '120.p1.e1'], 'core': '48.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 101, -1, 7553, -1, 1438, -1], 'generators': [1, 192, 488, 404], 'label': '960.10116.24.p1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.e1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319496
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.f1', '12.h1.b1', '12.x1.b1', '12.x1.e1'], 'contains': ['48.b1.c1', '48.k1.b1', '48.l1.d1', '120.p1.f1'], 'core': '48.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 1546, -1, 7553, -1, 1322, -1], 'generators': [1, 192, 488, 884], 'label': '960.10116.24.p1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.f1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319497
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.g1', '12.h1.b1', '12.x1.d1', '12.x1.g1'], 'contains': ['48.b1.d1', '48.k1.a1', '48.l1.d1', '120.p1.g1'], 'core': '48.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 1903, -1, 7553, -1, 2396, -1], 'generators': [481, 192, 488, 404], 'label': '960.10116.24.p1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.g1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319498
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.h1', '12.h1.b1', '12.x1.c1', '12.x1.h1'], 'contains': ['48.b1.d1', '48.k1.b1', '48.l1.b1', '120.p1.h1'], 'core': '48.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [8036, -1, 389, -1, 7553, -1, 922, -1], 'generators': [481, 192, 488, 884], 'label': '960.10116.24.p1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.h1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319499
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.k1.a1', '12.x1.a1', '12.x1.g1'], 'contains': ['48.c1.a1', '48.j1.a1', '48.k1.a1', '120.q1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9791, -1, 2574, -1, 8588, -1, 1933, -1], 'generators': [3, 192, 488, 404], 'label': '960.10116.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319500
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.k1.a1', '12.x1.c1', '12.x1.e1'], 'contains': ['48.c1.b1', '48.j1.a1', '48.k1.b1', '120.q1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9791, -1, 1299, -1, 8588, -1, 1817, -1], 'generators': [483, 192, 488, 884], 'label': '960.10116.24.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319501
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.c1', '12.k1.a1', '12.x1.b1', '12.x1.h1'], 'contains': ['48.c1.a1', '48.j1.b1', '48.k1.b1', '120.q1.c1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9791, -1, 567, -1, 8588, -1, 859, -1], 'generators': [3, 192, 488, 884], 'label': '960.10116.24.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319502
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.d1', '12.k1.a1', '12.x1.d1', '12.x1.f1'], 'contains': ['48.c1.b1', '48.j1.b1', '48.k1.a1', '120.q1.d1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9791, -1, 911, -1, 8588, -1, 2333, -1], 'generators': [483, 192, 488, 404], 'label': '960.10116.24.q1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319503
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.h1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.k1.a1', '8.t1.a1', '8.t1.b1', '12.j1.a1', '20.h1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1254, 2184, 8272, 7443, 959, 7312, 8849, 1615], 'generators': [7, 640, 240, 192, 488, 480], 'label': '960.10116.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.k1.a1', '20.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319504
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.q1.a1', '12.x1.a1', '12.x1.h1'], 'contains': ['48.c1.a1', '48.l1.a1', '48.l1.b1', '120.r1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9941, -1, 48, -1, 9130, -1, 980, -1], 'generators': [405, 192, 488, 406], 'label': '960.10116.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319505
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '12.q1.a1', '12.x1.b1', '12.x1.g1'], 'contains': ['48.c1.a1', '48.l1.c1', '48.l1.d1', '120.r1.b1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9941, -1, 1851, -1, 9130, -1, 1707, -1], 'generators': [885, 192, 488, 886], 'label': '960.10116.24.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319506
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.c1', '12.q1.a1', '12.x1.d1', '12.x1.e1'], 'contains': ['48.c1.b1', '48.l1.a1', '48.l1.d1', '120.r1.c1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9941, -1, 1790, -1, 9130, -1, 2275, -1], 'generators': [885, 192, 488, 406], 'label': '960.10116.24.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319507
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.25', 'aut_weyl_index': 384, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.d1', '12.q1.a1', '12.x1.c1', '12.x1.f1'], 'contains': ['48.c1.b1', '48.l1.b1', '48.l1.c1', '120.r1.d1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9941, -1, 468, -1, 9130, -1, 1601, -1], 'generators': [405, 192, 488, 886], 'label': '960.10116.24.r1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319508
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '12.a1.a1'], 'contains': ['48.d1.a1', '48.m1.a1', '48.o1.a1', '120.s1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1558, -1, 8815, -1, 1159, -1, 9168, -1], 'generators': [2, 192, 480, 240], 'label': '960.10116.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.s1.a1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319509
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.b1', '12.a1.a1'], 'contains': ['48.d1.b1', '48.m1.a1', '48.o1.a1', '120.s1.b1'], 'core': '48.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1558, -1, 8872, -1, 1159, -1, 9105, -1], 'generators': [2, 192, 480, 728], 'label': '960.10116.24.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.s1.b1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319510
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.c1', '12.a1.b1'], 'contains': ['48.d1.a1', '48.m1.b1', '48.o1.b1', '120.s1.c1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1558, -1, 9341, -1, 1159, -1, 9657, -1], 'generators': [1, 192, 480, 240], 'label': '960.10116.24.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '24.s1.c1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319511
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.d1', '12.a1.b1'], 'contains': ['48.d1.b1', '48.m1.b1', '48.o1.b1', '120.s1.d1'], 'core': '48.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1558, -1, 9399, -1, 1159, -1, 9560, -1], 'generators': [1, 192, 480, 728], 'label': '960.10116.24.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '24.s1.d1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319512
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '12.j1.a1'], 'contains': ['48.d1.a1', '48.n1.a1', '48.p1.a1', '120.t1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [150, -1, 9203, -1, 719, -1, 9043, -1], 'generators': [7, 192, 480, 240], 'label': '960.10116.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.t1.a1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319513
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.b1', '12.j1.a1'], 'contains': ['48.d1.b1', '48.n1.a1', '48.p1.a1', '120.t1.b1'], 'core': '48.d1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [150, -1, 9259, -1, 719, -1, 8980, -1], 'generators': [7, 192, 480, 728], 'label': '960.10116.24.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.t1.b1', 'projective_image': '48.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319514
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.h1.a1', '8.o1.a1', '8.o1.b1', '8.o1.c1', '8.o1.d1', '12.k1.a1', '20.i1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8561, 6738, 3232, 3935, 7350, 4357, 3775, 6495], 'generators': [3, 640, 480, 192, 404, 488], 'label': '960.10116.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.h1.a1', '8.o1.b1', '8.o1.a1', '8.o1.d1', '8.o1.c1', '20.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319515
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 96, 'centralizer': '4.m1.a1', 'complements': ['32.e1.a1', '32.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.f1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.a1.b1', '60.b1.a1', '60.b1.b1', '60.c1.a1', '60.d1.a1', '60.e1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5949, 8807, 8418, 9342, 7404, 487, 8965, 389], 'generators': [1, 2, 240], 'label': '960.10116.30.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.f1.a1'], 'normal_contains': ['60.a1.b1', '60.a1.a1', '60.b1.b1', '60.b1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319516
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.f1.a1', '60.i1.a1', '60.j1.a1', '60.l1.a1', '60.o1.b1', '60.u1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1750, -1, 6973, -1, 5052, -1, 8913, -1], 'generators': [5, 2, 240], 'label': '960.10116.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319517
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.a1.b1', '15.a1.a1'], 'contains': ['60.a1.b1', '60.f1.b1', '60.i1.b1', '60.j1.a1', '60.l1.b1', '60.o1.a1', '60.u1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [1750, -1, 8187, -1, 5052, -1, 8860, -1], 'generators': [1, 6, 240], 'label': '960.10116.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.b1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319518
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.f1.a1', '60.g1.a1', '60.l1.b1', '60.m1.a1', '60.s1.b1', '60.w1.b1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4849, -1, 7296, -1, 5532, -1, 6927, -1], 'generators': [241, 2, 4], 'label': '960.10116.30.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319519
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.b1.b1', '60.f1.b1', '60.g1.b1', '60.l1.a1', '60.m1.a1', '60.s1.a1', '60.w1.a1'], 'core': '60.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4849, -1, 6307, -1, 5532, -1, 6552, -1], 'generators': [1, 242, 4], 'label': '960.10116.30.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.c1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319520
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.g1.a1', '60.h1.a1', '60.n1.a1', '60.o1.a1', '60.s1.a1', '60.t1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6778, -1, 7856, -1, 6278, -1, 7520, -1], 'generators': [2, 4, 240], 'label': '960.10116.30.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319521
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '10.c1.b1', '15.a1.a1'], 'contains': ['60.a1.b1', '60.g1.b1', '60.h1.b1', '60.n1.a1', '60.o1.b1', '60.s1.b1', '60.t1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6778, -1, 6358, -1, 6278, -1, 8118, -1], 'generators': [1, 4, 240], 'label': '960.10116.30.d1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.d1.b1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319522
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '10.d1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.h1.a1', '60.i1.a1', '60.t1.b1', '60.u1.b1', '60.v1.a1', '60.w1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3650, -1, 7066, -1, 6150, -1, 8182, -1], 'generators': [241, 2, 404], 'label': '960.10116.30.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319523
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '10.d1.b1', '15.a1.a1'], 'contains': ['60.b1.b1', '60.h1.b1', '60.i1.b1', '60.t1.a1', '60.u1.a1', '60.v1.a1', '60.w1.b1'], 'core': '60.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3650, -1, 7640, -1, 6150, -1, 7724, -1], 'generators': [1, 242, 404], 'label': '960.10116.30.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.e1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319524
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '10.e1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '60.f1.a1', '60.f1.b1', '60.h1.a1', '60.h1.b1', '60.k1.a1', '60.q1.a1', '60.x1.a1', '60.x1.b1', '60.x1.c1', '60.x1.d1', '60.x1.e1', '60.x1.f1', '60.x1.g1', '60.x1.h1'], 'core': '60.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9141, -1, 4057, -1, 9119, -1, 4252, -1], 'generators': [1, 2, 404, 480], 'label': '960.10116.30.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.f1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319589
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '20.d1.a1'], 'contains': ['80.b1.b1', '80.i1.a1', '80.l1.a1', '120.m1.b1'], 'core': '80.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5258, -1, 6258, -1, 2082, -1, 5159, -1], 'generators': [2, 484, 8, 640], 'label': '960.10116.40.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '40.q1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.q1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319525
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.j1.b1', '12.l1.a1', '20.j1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2125, 3672, 5152, 7619, 1761, 5299, 5473, 3161], 'generators': [5, 640, 192, 8, 242, 480], 'label': '960.10116.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.a1', '8.j1.b1', '20.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319526
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '10.g1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '60.g1.a1', '60.g1.b1', '60.i1.a1', '60.i1.b1', '60.p1.a1', '60.r1.a1'], 'core': '60.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7816, -1, 4921, -1, 8251, -1, 6875, -1], 'generators': [1, 2, 4], 'label': '960.10116.30.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.g1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319527
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.267', 'aut_weyl_index': 192, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '10.h1.a1', '15.a1.a1'], 'contains': ['60.d1.a1', '60.j1.a1', '60.k1.a1', '60.m1.a1', '60.n1.a1', '60.p1.a1', '60.v1.a1'], 'core': '60.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5545, -1, 8286, -1, 6789, -1, 8687, -1], 'generators': [3, 4, 240], 'label': '960.10116.30.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.h1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319528
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '10.i1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '60.k1.a1', '60.l1.a1', '60.l1.b1', '60.r1.a1', '60.t1.a1', '60.t1.b1'], 'core': '60.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8241, -1, 5178, -1, 7923, -1, 7585, -1], 'generators': [241, 242, 404], 'label': '960.10116.30.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.i1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319529
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '10.j1.a1', '15.a1.a1'], 'contains': ['60.d1.a1', '60.o1.a1', '60.o1.b1', '60.q1.a1', '60.r1.a1', '60.w1.a1', '60.w1.b1'], 'core': '60.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7586, -1, 5443, -1, 8043, -1, 7043, -1], 'generators': [5, 6, 240], 'label': '960.10116.30.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.j1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319530
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '30.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 96, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '10.k1.a1', '15.a1.a1'], 'contains': ['60.e1.a1', '60.p1.a1', '60.q1.a1', '60.s1.a1', '60.s1.b1', '60.u1.a1', '60.u1.b1'], 'core': '60.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8447, -1, 8573, -1, 8147, -1, 8744, -1], 'generators': [241, 242, 4], 'label': '960.10116.30.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.k1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319531
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '32.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.i1.a1', '16.i1.b1', '16.j1.a1', '16.k1.a1', '16.l1.a1', '16.l1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '160.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2372, 3708, 5684, 4600, 2258, 4649, 4461, 3698], 'generators': [8, 192, 640], 'label': '960.10116.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.215', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.13', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319532
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '32.b1', 'aut_quo_index': 672, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.c1.a1', '16.c1.b1', '16.c1.c1', '16.c1.d1', '16.d1.a1', '16.d1.b1', '16.e1.a1', '16.e1.b1', '16.f1.a1', '16.f1.b1', '16.g1.a1', '16.g1.b1', '16.g1.c1', '16.g1.d1'], 'contains': ['64.a1.a1', '96.b1.a1', '160.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7266, 7410, 1292, 2322, 6785, 2992, 540, 7898], 'generators': [488, 192, 640], 'label': '960.10116.32.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.d1', '16.c1.a1', '16.c1.b1', '16.c1.c1', '16.d1.a1', '16.d1.b1', '16.e1.b1', '16.e1.a1', '16.f1.b1', '16.f1.a1', '16.g1.a1', '16.g1.c1', '16.g1.b1', '16.g1.d1'], 'normal_contains': ['64.a1.a1', '96.b1.a1', '160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319533
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '32.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.a1', '16.h1.b1', '16.m1.a1', '16.m1.b1', '16.n1.a1', '16.o1.a1', '16.o1.b1', '16.p1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '160.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [641, 2688, 9711, 8841, 1308, 3531, 9194, 3081], 'generators': [480, 192, 640], 'label': '960.10116.32.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.h1.b1', '16.h1.a1'], 'normal_contains': ['64.a1.a1', '96.c1.a1', '160.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '96.210', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319534
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.i1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.d1.a1', '160.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2502, -1, 5403, -1, 2136, -1, 4296, -1], 'generators': [2, 192, 640], 'label': '960.10116.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.d1.a1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319535
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '16.i1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.d1.b1', '160.d1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2502, -1, 5110, -1, 2136, -1, 4364, -1], 'generators': [482, 192, 640], 'label': '960.10116.32.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.d1.b1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319536
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.e1.b1', '8.j1.a1', '12.l1.b1', '20.j1.b1'], 'core': '4.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2125, 3672, 6461, 7882, 1761, 5299, 5802, 3733], 'generators': [241, 640, 192, 488, 6, 480], 'label': '960.10116.4.j1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.b1', '8.j1.a1', '20.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319537
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.c1', '16.i1.b1', '16.m1.b1'], 'contains': ['64.a1.a1', '96.d1.c1', '160.d1.c1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2502, -1, 3723, -1, 2136, -1, 4262, -1], 'generators': [1, 192, 640], 'label': '960.10116.32.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '32.d1.c1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319538
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.d1', '16.i1.b1', '16.m1.b1'], 'contains': ['64.a1.a1', '96.d1.d1', '160.d1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2502, -1, 3692, -1, 2136, -1, 4330, -1], 'generators': [481, 192, 640], 'label': '960.10116.32.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '32.d1.d1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319539
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.j1.a1', '16.n1.a1'], 'contains': ['64.a1.a1', '96.e1.a1', '160.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [389, -1, 6421, -1, 2051, -1, 4556, -1], 'generators': [407, 640, 192], 'label': '960.10116.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.e1.a1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319540
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.5', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.j1.a1', '16.n1.a1'], 'contains': ['64.a1.a1', '96.e1.b1', '160.e1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [389, -1, 6481, -1, 2051, -1, 4504, -1], 'generators': [887, 640, 192], 'label': '960.10116.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.e1.b1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319590
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.c1', '20.d1.b1'], 'contains': ['80.b1.a1', '80.i1.b1', '80.l1.b1', '120.m1.c1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5258, -1, 4215, -1, 2082, -1, 4966, -1], 'generators': [1, 4, 8, 640], 'label': '960.10116.40.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '40.q1.c1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.q1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319541
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '40.a1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1', '20.e1.a1', '20.f1.a1', '20.g1.a1'], 'contains': ['80.a1.a1', '80.c1.a1', '80.c1.b1', '80.i1.a1', '80.m1.a1', '120.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3819, 4629, 5294, 6186, 3073, 4098, 6559, 4236], 'generators': [2, 488, 480, 640], 'label': '960.10116.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1', '20.e1.a1', '20.d1.a1', '20.f1.a1', '20.g1.a1'], 'normal_contains': ['80.a1.a1', '80.c1.a1', '80.c1.b1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '240.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319542
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '40.a1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '20.a1.b1', '20.b1.b1', '20.c1.b1', '20.d1.b1', '20.e1.b1', '20.f1.b1', '20.g1.a1'], 'contains': ['80.a1.a1', '80.c1.c1', '80.c1.d1', '80.i1.b1', '80.m1.b1', '120.a1.b1'], 'core': '40.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3819, 4629, 4609, 5722, 3073, 4098, 6434, 3805], 'generators': [1, 488, 480, 640], 'label': '960.10116.40.a1.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.a1.b1', 'normal_contained_in': ['8.a1.b1', '20.a1.b1', '20.b1.b1', '20.c1.b1', '20.e1.b1', '20.d1.b1', '20.f1.b1', '20.g1.a1'], 'normal_contains': ['80.a1.a1', '80.c1.d1', '80.c1.c1', '120.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.b1', 'projective_image': '240.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319543
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '40.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.a1.a1', '20.a1.b1', '20.h1.a1', '20.i1.a1', '20.j1.a1', '20.j1.b1', '20.k1.a1'], 'contains': ['80.a1.a1', '80.d1.a1', '80.d1.b1', '80.j1.a1', '80.n1.a1', '120.g1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2969, 3551, 4743, 5237, 2581, 5677, 6373, 4669], 'generators': [407, 488, 480, 640], 'label': '960.10116.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.b1.a1', '20.a1.b1', '20.a1.a1', '20.h1.a1', '20.j1.a1', '20.j1.b1', '20.k1.a1', '20.i1.a1'], 'normal_contains': ['80.a1.a1', '80.d1.a1', '80.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319544
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '40.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.b1.a1', '20.b1.b1', '20.h1.a1', '20.l1.a1', '20.m1.a1', '20.n1.a1', '20.n1.b1'], 'contains': ['80.a1.a1', '80.h1.a1', '80.h1.b1', '120.b1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3216, 1160, 9442, 7988, 2459, 4815, 8917, 1976], 'generators': [488, 240, 640, 480], 'label': '960.10116.40.c1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.c1.a1', 'normal_contained_in': ['8.c1.a1', '20.b1.b1', '20.b1.a1', '20.h1.a1', '20.l1.a1', '20.m1.a1', '20.n1.a1', '20.n1.b1'], 'normal_contains': ['80.a1.a1', '80.h1.b1', '80.h1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319545
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '40.d1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.g1.a1', '20.i1.a1', '20.l1.a1', '20.o1.a1', '20.p1.a1', '20.q1.a1', '20.r1.a1'], 'contains': ['80.a1.a1', '80.e1.a1', '80.e1.b1', '120.c1.a1'], 'core': '40.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8699, 5876, 4527, 5976, 7730, 3898, 6312, 3911], 'generators': [3, 480, 640, 488], 'label': '960.10116.40.d1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.d1.a1', 'normal_contained_in': ['8.d1.a1', '20.g1.a1', '20.i1.a1', '20.l1.a1', '20.o1.a1', '20.p1.a1', '20.q1.a1', '20.r1.a1'], 'normal_contains': ['80.a1.a1', '80.e1.b1', '80.e1.a1', '120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.d1.a1', 'projective_image': '240.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319546
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '40.e1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '20.b1.a1', '20.c1.b1', '20.j1.a1', '20.o1.a1', '20.s1.a1', '20.t1.a1', '20.u1.a1'], 'contains': ['80.a1.a1', '80.o1.a1', '120.d1.a1'], 'core': '40.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3376, 3303, 9039, 6906, 2827, 4611, 8348, 2298], 'generators': [242, 488, 640, 480], 'label': '960.10116.40.e1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.e1.a1', 'normal_contained_in': ['8.e1.a1', '20.b1.a1', '20.c1.b1', '20.j1.a1', '20.t1.a1', '20.s1.a1', '20.u1.a1', '20.o1.a1'], 'normal_contains': ['80.a1.a1', '120.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.e1.a1', 'projective_image': '240.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319547
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '4.k1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.h1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.g1.a1', '8.r1.a1', '8.r1.b1', '12.m1.a1', '20.k1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2804, 4960, 6551, 4679, 1607, 9621, 4789, 5413], 'generators': [731, 640, 480, 192, 4, 8], 'label': '960.10116.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.b1.b1', '2.b1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.g1.a1', '20.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319548
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '40.e1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '20.b1.b1', '20.c1.a1', '20.j1.b1', '20.o1.a1', '20.s1.b1', '20.t1.b1', '20.u1.b1'], 'contains': ['80.a1.a1', '80.o1.b1', '120.d1.b1'], 'core': '40.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3376, 3303, 8025, 8119, 2827, 4611, 8446, 2191], 'generators': [241, 488, 640, 480], 'label': '960.10116.40.e1.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.e1.b1', 'normal_contained_in': ['8.e1.b1', '20.b1.b1', '20.c1.a1', '20.j1.b1', '20.t1.b1', '20.s1.b1', '20.u1.b1', '20.o1.a1'], 'normal_contains': ['80.a1.a1', '120.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.e1.b1', 'projective_image': '240.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319549
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '40.f1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '20.c1.a1', '20.c1.b1', '20.k1.a1', '20.l1.a1', '20.v1.a1', '20.w1.a1', '20.w1.b1'], 'contains': ['80.a1.a1', '80.k1.a1', '120.e1.a1'], 'core': '40.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4006, 5276, 7534, 7417, 2951, 5249, 7620, 2084], 'generators': [731, 480, 640, 8], 'label': '960.10116.40.f1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.f1.a1', 'normal_contained_in': ['8.f1.a1', '20.c1.b1', '20.c1.a1', '20.k1.a1', '20.l1.a1', '20.v1.a1', '20.w1.a1', '20.w1.b1'], 'normal_contains': ['80.a1.a1', '120.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.f1.a1', 'projective_image': '240.206', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319550
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '40.g1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '20.d1.a1', '20.d1.b1', '20.k1.a1', '20.m1.a1', '20.p1.a1', '20.s1.a1', '20.s1.b1'], 'contains': ['80.a1.a1', '80.b1.a1', '80.b1.b1', '120.h1.a1'], 'core': '40.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5510, 1533, 7751, 4975, 3197, 8623, 7058, 3501], 'generators': [4, 480, 8, 640], 'label': '960.10116.40.g1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.g1.a1', 'normal_contained_in': ['8.g1.a1', '20.d1.b1', '20.d1.a1', '20.k1.a1', '20.m1.a1', '20.s1.a1', '20.s1.b1', '20.p1.a1'], 'normal_contains': ['80.a1.a1', '80.b1.a1', '80.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.g1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319551
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '40.h1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '20.e1.a1', '20.e1.b1', '20.i1.a1', '20.m1.a1', '20.t1.a1', '20.t1.b1', '20.v1.a1'], 'contains': ['80.a1.a1', '80.f1.a1', '80.f1.b1', '120.i1.a1'], 'core': '40.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6082, 4931, 5350, 5587, 3822, 5982, 6622, 4343], 'generators': [404, 480, 488, 640], 'label': '960.10116.40.h1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.h1.a1', 'normal_contained_in': ['8.h1.a1', '20.e1.b1', '20.e1.a1', '20.i1.a1', '20.m1.a1', '20.t1.a1', '20.t1.b1', '20.v1.a1'], 'normal_contains': ['80.a1.a1', '80.f1.b1', '80.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.h1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319552
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '40.i1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '20.a1.b1', '20.e1.a1', '20.n1.a1', '20.q1.a1', '20.s1.a1', '20.u1.b1', '20.w1.a1'], 'contains': ['80.a1.a1', '80.g1.a1', '80.g1.c1', '120.j1.a1'], 'core': '40.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6454, 4235, 5094, 5465, 3575, 5044, 6127, 4452], 'generators': [406, 480, 488, 640], 'label': '960.10116.40.i1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.i1.a1', 'normal_contained_in': ['8.i1.a1', '20.a1.b1', '20.e1.a1', '20.n1.a1', '20.s1.a1', '20.u1.b1', '20.w1.a1', '20.q1.a1'], 'normal_contains': ['80.a1.a1', '80.g1.a1', '80.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '40.i1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319553
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '40.i1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '20.a1.a1', '20.e1.b1', '20.n1.b1', '20.q1.a1', '20.s1.b1', '20.u1.a1', '20.w1.b1'], 'contains': ['80.a1.a1', '80.g1.b1', '80.g1.d1', '120.j1.b1'], 'core': '40.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6454, 4235, 5035, 5119, 3575, 5044, 6497, 4562], 'generators': [405, 480, 488, 640], 'label': '960.10116.40.i1.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.i1.b1', 'normal_contained_in': ['8.i1.b1', '20.a1.a1', '20.e1.b1', '20.n1.b1', '20.s1.b1', '20.u1.a1', '20.w1.b1', '20.q1.a1'], 'normal_contains': ['80.a1.a1', '80.g1.b1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.i1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319554
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '40.j1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '20.d1.a1', '20.f1.b1', '20.j1.b1', '20.n1.a1', '20.r1.a1', '20.t1.a1', '20.w1.b1'], 'contains': ['80.a1.a1', '80.l1.a1', '120.k1.a1'], 'core': '40.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4916, 2414, 7132, 7185, 3324, 6863, 7219, 3391], 'generators': [6, 480, 8, 640], 'label': '960.10116.40.j1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.j1.a1', 'normal_contained_in': ['8.j1.a1', '20.d1.a1', '20.f1.b1', '20.j1.b1', '20.n1.a1', '20.t1.a1', '20.w1.b1', '20.r1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.j1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319555
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '40.j1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.b1', '20.d1.b1', '20.f1.a1', '20.j1.a1', '20.n1.b1', '20.r1.a1', '20.t1.b1', '20.w1.a1'], 'contains': ['80.a1.a1', '80.l1.b1', '120.k1.b1'], 'core': '40.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4916, 2414, 5592, 7575, 3324, 6863, 7418, 3160], 'generators': [5, 480, 8, 640], 'label': '960.10116.40.j1.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.j1.b1', 'normal_contained_in': ['8.j1.b1', '20.d1.b1', '20.f1.a1', '20.j1.a1', '20.n1.b1', '20.t1.b1', '20.w1.a1', '20.r1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.j1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319556
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '40.k1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '20.f1.a1', '20.f1.b1', '20.h1.a1', '20.p1.a1', '20.u1.a1', '20.u1.b1', '20.v1.a1'], 'contains': ['80.a1.a1', '80.p1.a1', '120.l1.a1'], 'core': '40.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2162, 2061, 8955, 6508, 2333, 7595, 8546, 2407], 'generators': [7, 488, 480, 640], 'label': '960.10116.40.k1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.k1.a1', 'normal_contained_in': ['8.k1.a1', '20.f1.b1', '20.f1.a1', '20.h1.a1', '20.u1.a1', '20.u1.b1', '20.v1.a1', '20.p1.a1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.k1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319557
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '20.a1.a1', '20.x1.a1', '20.x1.c1'], 'contains': ['80.c1.a1', '80.d1.a1', '80.g1.b1', '120.o1.a1'], 'core': '40.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 2202, 636, 6969, 2951, 3022, 7024], 'generators': [405, 2, 488, 640], 'label': '960.10116.40.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.a1', 'normal_contained_in': ['8.l1.a1', '20.a1.a1', '20.x1.c1', '20.x1.a1'], 'normal_contains': ['80.c1.a1', '80.d1.a1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319558
    {'ambient': '960.10116', 'aut_centralizer_order': 96, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2319', 'aut_weyl_index': 96, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.f1.a1', '12.d1.a1', '20.l1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4427, 7710, 7929, 9056, 5818, 3324, 7331, 593], 'generators': [3, 480, 640, 192, 240, 488], 'label': '960.10116.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.d1.a1', '12.d1.a1', '20.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '24.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319559
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '20.a1.a1', '20.x1.b1', '20.x1.d1'], 'contains': ['80.c1.a1', '80.d1.b1', '80.g1.d1', '120.o1.b1'], 'core': '40.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 3061, 2366, 6969, 2951, 3282, 5984], 'generators': [885, 2, 488, 640], 'label': '960.10116.40.l1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.b1', 'normal_contained_in': ['8.l1.b1', '20.a1.a1', '20.x1.d1', '20.x1.b1'], 'normal_contains': ['80.c1.a1', '80.d1.b1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319560
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.c1', '20.a1.a1', '20.x1.e1', '20.x1.g1'], 'contains': ['80.c1.b1', '80.d1.a1', '80.g1.d1', '120.o1.c1'], 'core': '40.l1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 3539, 1222, 6969, 2951, 3834, 5354], 'generators': [885, 482, 488, 640], 'label': '960.10116.40.l1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.c1', 'normal_contained_in': ['8.l1.c1', '20.a1.a1', '20.x1.g1', '20.x1.e1'], 'normal_contains': ['80.c1.b1', '80.d1.a1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319561
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.d1', '20.a1.a1', '20.x1.f1', '20.x1.h1'], 'contains': ['80.c1.b1', '80.d1.b1', '80.g1.b1', '120.o1.d1'], 'core': '40.l1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 2157, 3861, 6969, 2951, 2786, 7266], 'generators': [405, 482, 488, 640], 'label': '960.10116.40.l1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.d1', 'normal_contained_in': ['8.l1.d1', '20.a1.a1', '20.x1.h1', '20.x1.f1'], 'normal_contains': ['80.c1.b1', '80.d1.b1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319562
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.e1', '20.a1.b1', '20.x1.a1', '20.x1.e1'], 'contains': ['80.c1.c1', '80.d1.a1', '80.g1.a1', '120.o1.e1'], 'core': '40.l1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 2549, 1634, 6969, 2951, 3158, 6257], 'generators': [1, 406, 488, 640], 'label': '960.10116.40.l1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.e1', 'normal_contained_in': ['8.l1.e1', '20.a1.b1', '20.x1.a1', '20.x1.e1'], 'normal_contains': ['80.c1.c1', '80.d1.a1', '80.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.e1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319563
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.f1', '20.a1.b1', '20.x1.b1', '20.x1.f1'], 'contains': ['80.c1.c1', '80.d1.b1', '80.g1.c1', '120.o1.f1'], 'core': '40.l1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 2626, 4044, 6969, 2951, 2822, 6045], 'generators': [1, 886, 488, 640], 'label': '960.10116.40.l1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.f1', 'normal_contained_in': ['8.l1.f1', '20.a1.b1', '20.x1.b1', '20.x1.f1'], 'normal_contains': ['80.c1.c1', '80.d1.b1', '80.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.f1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319564
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.g1', '20.a1.b1', '20.x1.c1', '20.x1.g1'], 'contains': ['80.c1.d1', '80.d1.a1', '80.g1.c1', '120.o1.g1'], 'core': '40.l1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 3231, 569, 6969, 2951, 3681, 5923], 'generators': [481, 886, 488, 640], 'label': '960.10116.40.l1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.g1', 'normal_contained_in': ['8.l1.g1', '20.a1.b1', '20.x1.c1', '20.x1.g1'], 'normal_contains': ['80.c1.d1', '80.d1.a1', '80.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.g1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319624
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '24.i1.a1', '24.p1.b1', '24.p1.d1', '24.p1.f1', '24.p1.h1', '24.q1.b1', '24.q1.c1'], 'contains': ['96.b1.a1', '240.k1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8148, -1, 652, -1, 7342, -1, 1290, -1], 'generators': [884, 488, 192], 'label': '960.10116.48.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.k1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319565
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.h1', '20.a1.b1', '20.x1.d1', '20.x1.h1'], 'contains': ['80.c1.d1', '80.d1.b1', '80.g1.a1', '120.o1.h1'], 'core': '40.l1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [7188, 6735, 2581, 1879, 6969, 2951, 3122, 7145], 'generators': [481, 406, 488, 640], 'label': '960.10116.40.l1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.l1.h1', 'normal_contained_in': ['8.l1.h1', '20.a1.b1', '20.x1.d1', '20.x1.h1'], 'normal_contains': ['80.c1.d1', '80.d1.b1', '80.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.l1.h1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.l1.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319566
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1', '24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '20.e1.a1', '20.x1.a1', '20.x1.d1'], 'contains': ['80.c1.a1', '80.f1.a1', '80.g1.a1', '120.p1.a1'], 'core': '40.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 2247, 1438, 7427, 3113, 3631, 6342], 'generators': [2, 404, 488, 640], 'label': '960.10116.40.m1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.a1', 'normal_contained_in': ['8.m1.a1', '20.e1.a1', '20.x1.d1', '20.x1.a1'], 'normal_contains': ['80.c1.a1', '80.f1.a1', '80.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319567
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.d1', '24.m1.c1', '24.t1.a1', '24.t1.b1', '24.n1.b1', '24.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '20.e1.a1', '20.x1.b1', '20.x1.c1'], 'contains': ['80.c1.a1', '80.f1.b1', '80.g1.c1', '120.p1.b1'], 'core': '40.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 2775, 1756, 7427, 3113, 2736, 6562], 'generators': [2, 884, 488, 640], 'label': '960.10116.40.m1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.b1', 'normal_contained_in': ['8.m1.b1', '20.e1.a1', '20.x1.c1', '20.x1.b1'], 'normal_contains': ['80.c1.a1', '80.f1.b1', '80.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319568
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1', '24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.c1', '20.e1.a1', '20.x1.f1', '20.x1.g1'], 'contains': ['80.c1.b1', '80.f1.a1', '80.g1.c1', '120.p1.c1'], 'core': '40.m1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 2894, 3121, 7427, 3113, 3784, 5838], 'generators': [482, 404, 488, 640], 'label': '960.10116.40.m1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.c1', 'normal_contained_in': ['8.m1.c1', '20.e1.a1', '20.x1.g1', '20.x1.f1'], 'normal_contains': ['80.c1.b1', '80.f1.a1', '80.g1.c1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319569
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '4.m1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.c1.b1', '2.h1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.h1.a1', '12.n1.a1', '20.m1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4863, 1850, 7471, 5034, 3517, 9891, 6745, 5015], 'generators': [4, 640, 192, 8, 240, 480], 'label': '960.10116.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.c1.b1', '2.c1.a1', '2.h1.a1'], 'normal_contains': ['8.c1.a1', '8.h1.a1', '8.g1.a1', '20.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319570
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': ['24.s1.c1', '24.s1.d1', '24.m1.d1', '24.m1.c1', '24.t1.a1', '24.t1.b1', '24.n1.b1', '24.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.d1', '20.e1.a1', '20.x1.e1', '20.x1.h1'], 'contains': ['80.c1.b1', '80.f1.b1', '80.g1.a1', '120.p1.d1'], 'core': '40.m1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 2718, 1974, 7427, 3113, 2907, 6939], 'generators': [482, 884, 488, 640], 'label': '960.10116.40.m1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.d1', 'normal_contained_in': ['8.m1.d1', '20.e1.a1', '20.x1.h1', '20.x1.e1'], 'normal_contains': ['80.c1.b1', '80.f1.b1', '80.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319571
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.e1', '20.e1.b1', '20.x1.a1', '20.x1.f1'], 'contains': ['80.c1.c1', '80.f1.a1', '80.g1.b1', '120.p1.e1'], 'core': '40.m1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 2111, 3440, 7427, 3113, 3072, 6452], 'generators': [1, 404, 488, 640], 'label': '960.10116.40.m1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.e1', 'normal_contained_in': ['8.m1.e1', '20.e1.b1', '20.x1.a1', '20.x1.f1'], 'normal_contains': ['80.c1.c1', '80.f1.a1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.e1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319572
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.b1', '24.m1.a1', '24.t1.a1', '24.t1.b1', '24.n1.b1', '24.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.f1', '20.e1.b1', '20.x1.b1', '20.x1.e1'], 'contains': ['80.c1.c1', '80.f1.b1', '80.g1.d1', '120.p1.f1'], 'core': '40.m1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 3180, 2461, 7427, 3113, 2972, 5728], 'generators': [1, 884, 488, 640], 'label': '960.10116.40.m1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.f1', 'normal_contained_in': ['8.m1.f1', '20.e1.b1', '20.x1.b1', '20.x1.e1'], 'normal_contains': ['80.c1.c1', '80.f1.b1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.f1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319573
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.g1', '20.e1.b1', '20.x1.d1', '20.x1.g1'], 'contains': ['80.c1.d1', '80.f1.a1', '80.g1.d1', '120.p1.g1'], 'core': '40.m1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 3472, 1316, 7427, 3113, 4043, 5529], 'generators': [481, 404, 488, 640], 'label': '960.10116.40.m1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.g1', 'normal_contained_in': ['8.m1.g1', '20.e1.b1', '20.x1.d1', '20.x1.g1'], 'normal_contains': ['80.c1.d1', '80.f1.a1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.g1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319574
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.b1', '24.m1.a1', '24.t1.a1', '24.t1.b1', '24.n1.b1', '24.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.h1', '20.e1.b1', '20.x1.c1', '20.x1.h1'], 'contains': ['80.c1.d1', '80.f1.b1', '80.g1.b1', '120.p1.h1'], 'core': '40.m1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [8348, 7288, 2366, 1058, 7427, 3113, 2547, 7352], 'generators': [481, 884, 488, 640], 'label': '960.10116.40.m1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.m1.h1', 'normal_contained_in': ['8.m1.h1', '20.e1.b1', '20.x1.c1', '20.x1.h1'], 'normal_contains': ['80.c1.d1', '80.f1.b1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.m1.h1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.m1.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319575
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '8.c1.a1', 'complements': ['24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '20.g1.a1', '20.x1.a1', '20.x1.b1'], 'contains': ['80.c1.a1', '80.c1.c1', '80.e1.a1', '120.f1.a1'], 'core': '40.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 8230, 2299, 1550, 8841, 2170, 2677, 5278], 'generators': [1, 2, 640, 488], 'label': '960.10116.40.n1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.n1.a1', 'normal_contained_in': ['8.n1.a1', '20.g1.a1', '20.x1.a1', '20.x1.b1'], 'normal_contains': ['80.c1.a1', '80.c1.c1', '80.e1.a1', '120.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.n1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319576
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '8.c1.a1', 'complements': ['24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '20.g1.a1', '20.x1.c1', '20.x1.d1'], 'contains': ['80.c1.a1', '80.c1.d1', '80.e1.b1', '120.f1.b1'], 'core': '40.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 8230, 3020, 484, 8841, 2170, 3725, 6121], 'generators': [481, 2, 640, 488], 'label': '960.10116.40.n1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.n1.b1', 'normal_contained_in': ['8.n1.b1', '20.g1.a1', '20.x1.c1', '20.x1.d1'], 'normal_contains': ['80.c1.d1', '80.c1.a1', '80.e1.b1', '120.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.n1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.n1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319577
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '8.c1.a1', 'complements': ['24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.c1', '20.g1.a1', '20.x1.e1', '20.x1.f1'], 'contains': ['80.c1.b1', '80.c1.c1', '80.e1.b1', '120.f1.c1'], 'core': '40.n1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 8230, 2973, 2759, 8841, 2170, 3572, 5429], 'generators': [1, 482, 640, 488], 'label': '960.10116.40.n1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.n1.c1', 'normal_contained_in': ['8.n1.c1', '20.g1.a1', '20.x1.e1', '20.x1.f1'], 'normal_contains': ['80.c1.b1', '80.c1.c1', '80.e1.b1', '120.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '40.n1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.n1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319578
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.n1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '8.c1.a1', 'complements': ['24.t1.a1', '24.t1.b1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.d1', '20.g1.a1', '20.x1.g1', '20.x1.h1'], 'contains': ['80.c1.b1', '80.c1.d1', '80.e1.a1', '120.f1.d1'], 'core': '40.n1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 8230, 2841, 720, 8841, 2170, 3202, 5126], 'generators': [481, 482, 640, 488], 'label': '960.10116.40.n1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.n1.d1', 'normal_contained_in': ['8.n1.d1', '20.g1.a1', '20.x1.g1', '20.x1.h1'], 'normal_contains': ['80.c1.d1', '80.c1.b1', '80.e1.a1', '120.f1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.n1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.n1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319579
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '20.i1.a1', '20.x1.a1', '20.x1.g1'], 'contains': ['80.d1.a1', '80.e1.a1', '80.f1.a1', '120.q1.a1'], 'core': '40.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9480, 7581, 2464, 948, 8475, 3302, 3449, 5629], 'generators': [3, 404, 488, 640], 'label': '960.10116.40.o1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.o1.a1', 'normal_contained_in': ['8.o1.a1', '20.i1.a1', '20.x1.g1', '20.x1.a1'], 'normal_contains': ['80.d1.a1', '80.e1.a1', '80.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.o1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319580
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.i1.a1', '8.j1.a1', '12.o1.a1', '20.n1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5781, 846, 7391, 8014, 2797, 5075, 5404, 3043], 'generators': [6, 640, 192, 8, 240, 480], 'label': '960.10116.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.i1.a1', '8.j1.a1', '20.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319581
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.b1', '24.m1.a1', '24.s1.c1', '24.s1.d1', '24.m1.d1', '24.m1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '20.i1.a1', '20.x1.c1', '20.x1.e1'], 'contains': ['80.d1.a1', '80.e1.b1', '80.f1.b1', '120.q1.b1'], 'core': '40.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9480, 7581, 3103, 848, 8475, 3302, 3397, 6750], 'generators': [483, 884, 488, 640], 'label': '960.10116.40.o1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.o1.b1', 'normal_contained_in': ['8.o1.b1', '20.i1.a1', '20.x1.c1', '20.x1.e1'], 'normal_contains': ['80.d1.a1', '80.e1.b1', '80.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.o1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.o1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319582
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.b1', '24.m1.a1', '24.s1.c1', '24.s1.d1', '24.m1.d1', '24.m1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.c1', '20.i1.a1', '20.x1.b1', '20.x1.h1'], 'contains': ['80.d1.b1', '80.e1.a1', '80.f1.b1', '120.q1.c1'], 'core': '40.o1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9480, 7581, 2418, 2257, 8475, 3302, 2453, 6839], 'generators': [3, 884, 488, 640], 'label': '960.10116.40.o1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.o1.c1', 'normal_contained_in': ['8.o1.c1', '20.i1.a1', '20.x1.h1', '20.x1.b1'], 'normal_contains': ['80.d1.b1', '80.e1.a1', '80.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.o1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.o1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319583
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.o1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.s1.c1', '24.s1.d1', '24.m1.c1', '24.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.d1', '20.i1.a1', '20.x1.d1', '20.x1.f1'], 'contains': ['80.d1.b1', '80.e1.b1', '80.f1.a1', '120.q1.d1'], 'core': '40.o1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9480, 7581, 2665, 4127, 8475, 3302, 3914, 6661], 'generators': [483, 404, 488, 640], 'label': '960.10116.40.o1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.o1.d1', 'normal_contained_in': ['8.o1.d1', '20.i1.a1', '20.x1.d1', '20.x1.f1'], 'normal_contains': ['80.d1.b1', '80.e1.b1', '80.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.o1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.o1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319584
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 256, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.s1.c1', '24.s1.d1', '24.t1.a1', '24.t1.b1', '24.m1.d1', '24.m1.c1', '24.n1.b1', '24.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '20.q1.a1', '20.x1.a1', '20.x1.h1'], 'contains': ['80.e1.a1', '80.g1.a1', '80.g1.b1', '120.r1.a1'], 'core': '40.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9601, 7758, 1935, 1154, 8753, 2627, 2598, 7206], 'generators': [405, 406, 488, 640], 'label': '960.10116.40.p1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.p1.a1', 'normal_contained_in': ['8.p1.a1', '20.q1.a1', '20.x1.h1', '20.x1.a1'], 'normal_contains': ['80.e1.a1', '80.g1.a1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.p1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319585
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 256, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.s1.c1', '24.s1.d1', '24.t1.a1', '24.t1.b1', '24.m1.c1', '24.m1.d1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '20.q1.a1', '20.x1.b1', '20.x1.g1'], 'contains': ['80.e1.a1', '80.g1.c1', '80.g1.d1', '120.r1.b1'], 'core': '40.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9601, 7758, 3396, 2093, 8753, 2627, 3246, 5202], 'generators': [885, 886, 488, 640], 'label': '960.10116.40.p1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.p1.b1', 'normal_contained_in': ['8.p1.b1', '20.q1.a1', '20.x1.g1', '20.x1.b1'], 'normal_contains': ['80.e1.a1', '80.g1.c1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.p1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319586
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 256, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.s1.c1', '24.s1.d1', '24.t1.a1', '24.t1.b1', '24.m1.d1', '24.m1.c1', '24.n1.b1', '24.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.p1.c1', '20.q1.a1', '20.x1.d1', '20.x1.e1'], 'contains': ['80.e1.b1', '80.g1.a1', '80.g1.d1', '120.r1.c1'], 'core': '40.p1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9601, 7758, 3329, 2161, 8753, 2627, 3870, 6196], 'generators': [885, 406, 488, 640], 'label': '960.10116.40.p1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.p1.c1', 'normal_contained_in': ['8.p1.c1', '20.q1.a1', '20.x1.d1', '20.x1.e1'], 'normal_contains': ['80.e1.b1', '80.g1.a1', '80.g1.d1'], 'normalizer': '1.a1.a1', 'old_label': '40.p1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.p1.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319587
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.p1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '48.38', 'aut_weyl_index': 256, 'centralizer': '24.b1.a1', 'complements': ['24.s1.a1', '24.s1.b1', '24.m1.a1', '24.m1.b1', '24.s1.c1', '24.s1.d1', '24.t1.a1', '24.t1.b1', '24.m1.c1', '24.m1.d1', '24.n1.a1', '24.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.p1.d1', '20.q1.a1', '20.x1.c1', '20.x1.f1'], 'contains': ['80.e1.b1', '80.g1.b1', '80.g1.c1', '120.r1.d1'], 'core': '40.p1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9601, 7758, 2517, 3345, 8753, 2627, 3317, 7084], 'generators': [405, 886, 488, 640], 'label': '960.10116.40.p1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.p1.d1', 'normal_contained_in': ['8.p1.d1', '20.q1.a1', '20.x1.c1', '20.x1.f1'], 'normal_contains': ['80.e1.b1', '80.g1.c1', '80.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '40.p1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.p1.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319588
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '20.d1.a1'], 'contains': ['80.b1.a1', '80.i1.a1', '80.l1.a1', '120.m1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5258, -1, 6315, -1, 2082, -1, 5094, -1], 'generators': [2, 4, 8, 640], 'label': '960.10116.40.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '40.q1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319591
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.i1.b1', '8.j1.b1', '12.o1.b1', '20.n1.b1'], 'core': '4.n1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5781, 846, 5384, 8298, 2797, 5075, 6670, 2437], 'generators': [5, 640, 192, 8, 240, 480], 'label': '960.10116.4.n1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.i1.b1', '8.j1.b1', '20.n1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.b1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319592
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '40.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.d1', '20.d1.b1'], 'contains': ['80.b1.b1', '80.i1.b1', '80.l1.b1', '120.m1.d1'], 'core': '80.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5258, -1, 4272, -1, 2082, -1, 5030, -1], 'generators': [1, 484, 8, 640], 'label': '960.10116.40.q1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '40.q1.d1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.q1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319593
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '20.k1.a1'], 'contains': ['80.b1.a1', '80.j1.a1', '80.k1.a1', '120.n1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2312, -1, 7316, -1, 1712, -1, 5280, -1], 'generators': [731, 4, 8, 640], 'label': '960.10116.40.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '40.r1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319594
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.b1', '20.k1.a1'], 'contains': ['80.b1.b1', '80.j1.a1', '80.k1.a1', '120.n1.b1'], 'core': '80.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2312, -1, 7363, -1, 1712, -1, 5332, -1], 'generators': [731, 484, 8, 640], 'label': '960.10116.40.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '40.r1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.r1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319595
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '20.b1.a1'], 'contains': ['80.h1.a1', '80.m1.a1', '80.o1.a1', '120.s1.a1'], 'core': '80.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1400, -1, 9617, -1, 1035, -1, 9720, -1], 'generators': [2, 240, 640, 480], 'label': '960.10116.40.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '40.s1.a1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319596
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.b1', '20.b1.a1'], 'contains': ['80.h1.b1', '80.m1.a1', '80.o1.a1', '120.s1.b1'], 'core': '80.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1400, -1, 9687, -1, 1035, -1, 9497, -1], 'generators': [2, 728, 640, 480], 'label': '960.10116.40.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '40.s1.b1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319597
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.c1', '20.b1.b1'], 'contains': ['80.h1.a1', '80.m1.b1', '80.o1.b1', '120.s1.c1'], 'core': '80.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1400, -1, 9904, -1, 1035, -1, 9914, -1], 'generators': [1, 240, 640, 480], 'label': '960.10116.40.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '40.s1.c1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.s1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319598
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '40.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 1536, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.d1', '20.b1.b1'], 'contains': ['80.h1.b1', '80.m1.b1', '80.o1.b1', '120.s1.d1'], 'core': '80.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1400, -1, 9974, -1, 1035, -1, 9817, -1], 'generators': [1, 728, 640, 480], 'label': '960.10116.40.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '40.s1.d1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.s1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319599
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '20.h1.a1'], 'contains': ['80.h1.a1', '80.n1.a1', '80.p1.a1', '120.t1.a1'], 'core': '80.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [619, -1, 9753, -1, 411, -1, 9405, -1], 'generators': [7, 240, 480, 640], 'label': '960.10116.40.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '40.t1.a1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319600
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '40.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 512, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.b1', '20.h1.a1'], 'contains': ['80.h1.b1', '80.n1.a1', '80.p1.a1', '120.t1.b1'], 'core': '80.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [619, -1, 9839, -1, 411, -1, 9289, -1], 'generators': [7, 728, 480, 640], 'label': '960.10116.40.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '40.t1.b1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.t1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319601
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '48.a1', 'aut_quo_index': 672, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.a1.b1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.j1.b1', '24.k1.a1', '24.k1.b1', '24.l1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '240.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3012, 6621, 5127, 8920, 4815, 1735, 6066, 2987], 'generators': [488, 192, 480], 'label': '960.10116.48.a1.a1', 'mobius_quo': -2, 'mobius_sub': -192, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.b1', '24.a1.a1', '24.b1.a1', '24.d1.a1', '24.d1.b1', '24.e1.a1', '24.c1.a1'], 'normal_contains': ['96.c1.a1', '96.a1.a1', '96.b1.a1', '240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.51', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319602
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['480.d1.c1', '480.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.j1.b1', '4.k1.a1', '4.s1.b1', '4.w1.b1', '6.c1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3636, 3717, 6428, 5694, 2995, 6657, 5300, 4712], 'generators': [241, 480, 4, 192, 2, 640, 488], 'label': '960.10116.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '4.j1.b1', '4.k1.a1', '4.s1.b1', '4.w1.b1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '48.51', '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': '24.14'}
  • id: 112319603
    {'ambient': '960.10116', 'aut_centralizer_order': 48, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.27015', 'aut_weyl_index': 48, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.e1.b1', '12.e1.a1', '20.o1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8390, 7132, 8032, 8734, 7060, 2157, 7655, 1345], 'generators': [241, 480, 640, 192, 242, 488], 'label': '960.10116.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.e1.b1', '8.d1.a1', '12.e1.a1', '20.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 112319604
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.f1.a1', '24.f1.b1', '24.o1.a1', '24.o1.b1', '24.p1.a1', '24.p1.b1'], 'contains': ['96.b1.a1', '96.d1.a1', '240.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7687, 8484, 384, 3837, 6985, 1089, 1813, 5103], 'generators': [2, 192, 488], 'label': '960.10116.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1', '24.f1.b1', '24.f1.a1'], 'normal_contains': ['96.b1.a1', '240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319605
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.a1.a1', '24.f1.c1', '24.f1.d1', '24.o1.c1', '24.o1.d1', '24.p1.c1', '24.p1.d1'], 'contains': ['96.b1.a1', '96.d1.b1', '240.b1.b1'], 'core': '48.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7687, 8484, 1487, 4253, 6985, 1089, 1910, 4733], 'generators': [482, 192, 488], 'label': '960.10116.48.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': ['16.c1.b1', '24.a1.a1', '24.f1.d1', '24.f1.c1'], 'normal_contains': ['96.b1.a1', '240.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319606
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.c1', '24.a1.b1', '24.f1.a1', '24.f1.c1', '24.o1.e1', '24.o1.f1', '24.p1.e1', '24.p1.f1'], 'contains': ['96.b1.a1', '96.d1.c1', '240.b1.c1'], 'core': '48.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7687, 8484, 831, 4429, 6985, 1089, 1653, 4888], 'generators': [1, 192, 488], 'label': '960.10116.48.b1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.c1', 'normal_contained_in': ['16.c1.c1', '24.a1.b1', '24.f1.a1', '24.f1.c1'], 'normal_contains': ['96.b1.a1', '240.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319607
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.d1', '24.a1.b1', '24.f1.b1', '24.f1.d1', '24.o1.g1', '24.o1.h1', '24.p1.g1', '24.p1.h1'], 'contains': ['96.b1.a1', '96.d1.d1', '240.b1.d1'], 'core': '48.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7687, 8484, 1614, 3550, 6985, 1089, 2036, 4995], 'generators': [481, 192, 488], 'label': '960.10116.48.b1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.d1', 'normal_contained_in': ['16.c1.d1', '24.a1.b1', '24.f1.b1', '24.f1.d1'], 'normal_contains': ['96.b1.a1', '240.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319608
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '48.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.c1.a1', '24.f1.a1', '24.f1.d1', '24.q1.a1', '24.q1.c1', '24.r1.a1', '24.r1.b1'], 'contains': ['96.b1.a1', '240.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9785, 9243, 1215, 4161, 8608, 932, 1605, 4555], 'generators': [3, 488, 192], 'label': '960.10116.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.e1.a1', '24.c1.a1', '24.f1.d1', '24.f1.a1'], 'normal_contains': ['96.b1.a1', '240.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319609
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '48.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.c1.a1', '24.f1.b1', '24.f1.c1', '24.q1.b1', '24.q1.d1', '24.r1.c1', '24.r1.d1'], 'contains': ['96.b1.a1', '240.c1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9785, 9243, 889, 3957, 8608, 932, 2119, 5186], 'generators': [483, 488, 192], 'label': '960.10116.48.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.b1', 'normal_contained_in': ['16.e1.b1', '24.c1.a1', '24.f1.b1', '24.f1.c1'], 'normal_contains': ['96.b1.a1', '240.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319610
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '48.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': ['20.x1.a1', '20.x1.d1', '20.x1.f1', '20.x1.g1', '20.x1.b1', '20.x1.c1', '20.x1.e1', '20.x1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.b1.a1', '24.s1.a1', '24.s1.c1', '24.t1.a1'], 'contains': ['96.c1.a1', '240.d1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [518, 3450, 9009, 9639, 1375, 2604, 9161, 1535], 'generators': [240, 480, 192], 'label': '960.10116.48.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.h1.a1', '24.b1.a1'], 'normal_contains': ['96.c1.a1', '240.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '48.39', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.39', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319611
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '48.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '1.a1.a1', 'complements': ['20.x1.b1', '20.x1.c1', '20.x1.e1', '20.x1.h1', '20.x1.a1', '20.x1.d1', '20.x1.f1', '20.x1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '24.b1.a1', '24.s1.b1', '24.s1.d1', '24.t1.b1'], 'contains': ['96.c1.a1', '240.d1.b1'], 'core': '48.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [518, 3450, 9197, 9574, 1375, 2604, 9074, 1388], 'generators': [728, 480, 192], 'label': '960.10116.48.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.d1.b1', 'normal_contained_in': ['16.h1.b1', '24.b1.a1'], 'normal_contains': ['96.c1.a1', '240.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.b1', 'projective_image': '48.39', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.39', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319612
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.a1.a1', '24.m1.a1', '24.m1.b1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.d1.b1', '240.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2821, -1, 5474, -1, 2960, -1, 4614, -1], 'generators': [2, 192, 8], 'label': '960.10116.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.e1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319613
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.a1.b1', '24.m1.c1', '24.m1.d1'], 'contains': ['96.a1.a1', '96.d1.c1', '96.d1.d1', '240.e1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2821, -1, 3798, -1, 2960, -1, 4412, -1], 'generators': [1, 192, 8], 'label': '960.10116.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.e1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319614
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '4.p1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.d1.a1', '8.g1.a1', '8.k1.a1', '12.p1.a1', '20.p1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7620, 2776, 7756, 5609, 5954, 9158, 6531, 4887], 'generators': [3, 640, 192, 488, 4, 480], 'label': '960.10116.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.k1.a1', '20.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319615
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.g1.a1', '24.n1.a1', '24.n1.b1'], 'contains': ['96.a1.a1', '96.e1.a1', '96.e1.b1', '240.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [769, -1, 6487, -1, 2354, -1, 4813, -1], 'generators': [407, 192, 8], 'label': '960.10116.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.f1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319616
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.e1.a1', '24.n1.a1', '24.n1.b1'], 'contains': ['96.a1.a1', '240.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1109, -1, 6816, -1, 2761, -1, 4914, -1], 'generators': [731, 8, 192], 'label': '960.10116.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.g1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319617
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.h1.a1', '24.m1.a1', '24.m1.c1', '24.n1.a1'], 'contains': ['96.a1.a1', '240.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4610, -1, 6377, -1, 3160, -1, 4696, -1], 'generators': [4, 8, 192], 'label': '960.10116.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319618
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.h1.a1', '24.m1.b1', '24.m1.d1', '24.n1.b1'], 'contains': ['96.a1.a1', '240.h1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4610, -1, 6575, -1, 3160, -1, 4730, -1], 'generators': [484, 8, 192], 'label': '960.10116.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.h1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319619
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.k1.a1', '24.m1.a1', '24.m1.b1'], 'contains': ['96.a1.a1', '240.i1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4474, -1, 5987, -1, 3227, -1, 4764, -1], 'generators': [6, 8, 192], 'label': '960.10116.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.i1.a1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319620
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '24.k1.b1', '24.m1.c1', '24.m1.d1'], 'contains': ['96.a1.a1', '240.i1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4474, -1, 3881, -1, 3227, -1, 4662, -1], 'generators': [5, 8, 192], 'label': '960.10116.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.i1.b1', 'projective_image': '96.215', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319621
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.g1.a1', '24.o1.a1', '24.o1.c1', '24.o1.e1', '24.o1.g1', '24.q1.a1', '24.q1.b1'], 'contains': ['96.b1.a1', '96.e1.a1', '240.j1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6453, -1, 1763, -1, 6689, -1, 1973, -1], 'generators': [407, 192, 488], 'label': '960.10116.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319622
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.g1.a1', '24.o1.b1', '24.o1.d1', '24.o1.f1', '24.o1.h1', '24.q1.c1', '24.q1.d1'], 'contains': ['96.b1.a1', '96.e1.b1', '240.j1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6453, -1, 547, -1, 6689, -1, 1716, -1], 'generators': [887, 192, 488], 'label': '960.10116.48.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.j1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319623
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.i1.a1', '24.p1.a1', '24.p1.c1', '24.p1.e1', '24.p1.g1', '24.q1.a1', '24.q1.d1'], 'contains': ['96.b1.a1', '240.k1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8148, -1, 1153, -1, 7342, -1, 2158, -1], 'generators': [404, 488, 192], 'label': '960.10116.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.k1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319625
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.q1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '768.327978', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.d1.a1', '8.i1.a1', '8.i1.b1', '8.p1.a1', '8.p1.b1', '8.p1.c1', '8.p1.d1', '12.q1.a1', '20.q1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8975, 7433, 3345, 4093, 8356, 2399, 3234, 6766], 'generators': [405, 640, 480, 192, 406, 488], 'label': '960.10116.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.e1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.d1.a1', '8.i1.a1', '8.i1.b1', '8.p1.c1', '8.p1.d1', '8.p1.a1', '8.p1.b1', '20.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319626
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.j1.a1', '24.o1.e1', '24.o1.h1', '24.p1.a1', '24.p1.d1', '24.r1.a1', '24.r1.c1'], 'contains': ['96.b1.a1', '240.l1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7328, -1, 474, -1, 7275, -1, 1765, -1], 'generators': [406, 488, 192], 'label': '960.10116.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.l1.a1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319627
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '24.j1.b1', '24.o1.a1', '24.o1.d1', '24.p1.e1', '24.p1.h1', '24.r1.a1', '24.r1.d1'], 'contains': ['96.b1.a1', '240.l1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7328, -1, 126, -1, 7275, -1, 1409, -1], 'generators': [405, 488, 192], 'label': '960.10116.48.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.l1.b1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319628
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.c1', '24.j1.a1', '24.o1.f1', '24.o1.g1', '24.p1.b1', '24.p1.c1', '24.r1.b1', '24.r1.d1'], 'contains': ['96.b1.a1', '240.l1.c1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7328, -1, 997, -1, 7275, -1, 1862, -1], 'generators': [886, 488, 192], 'label': '960.10116.48.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.l1.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319629
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.d1', '24.j1.b1', '24.o1.b1', '24.o1.c1', '24.p1.f1', '24.p1.g1', '24.r1.b1', '24.r1.c1'], 'contains': ['96.b1.a1', '240.l1.d1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7328, -1, 1557, -1, 7275, -1, 2085, -1], 'generators': [885, 488, 192], 'label': '960.10116.48.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.l1.d1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319630
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.a1.a1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.c1.a1', '96.d1.a1', '96.d1.b1', '240.m1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1520, -1, 8732, -1, 1937, -1, 8657, -1], 'generators': [2, 192, 480], 'label': '960.10116.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.m1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319631
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '24.a1.b1', '24.s1.c1', '24.s1.d1'], 'contains': ['96.c1.a1', '96.d1.c1', '96.d1.d1', '240.m1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1520, -1, 9306, -1, 1937, -1, 8921, -1], 'generators': [1, 192, 480], 'label': '960.10116.48.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.m1.b1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319632
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.g1.a1', '24.t1.a1', '24.t1.b1'], 'contains': ['96.c1.a1', '96.e1.a1', '96.e1.b1', '240.n1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [84, -1, 9108, -1, 1471, -1, 8594, -1], 'generators': [407, 192, 480], 'label': '960.10116.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.n1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319633
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '24.d1.a1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.c1.a1', '240.o1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1269, -1, 8894, -1, 1634, -1, 8872, -1], 'generators': [242, 480, 192], 'label': '960.10116.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.o1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319634
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '24.d1.b1', '24.s1.c1', '24.s1.d1'], 'contains': ['96.c1.a1', '240.o1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1269, -1, 9390, -1, 1634, -1, 9384, -1], 'generators': [241, 480, 192], 'label': '960.10116.48.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.o1.b1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319635
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '24.l1.a1', '24.t1.a1', '24.t1.b1'], 'contains': ['96.c1.a1', '240.p1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [214, -1, 9166, -1, 1186, -1, 8786, -1], 'generators': [7, 480, 192], 'label': '960.10116.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.p1.a1', 'projective_image': '96.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319636
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.r1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '768.327978', 'aut_weyl_index': 16, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.d1.a1', '8.j1.a1', '8.j1.b1', '12.r1.a1', '20.r1.a1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7773, 6404, 4466, 8156, 7514, 4626, 4873, 4072], 'generators': [5, 640, 192, 8, 6, 480], 'label': '960.10116.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.d1.a1', '8.j1.a1', '8.j1.b1', '20.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319637
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '60.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.b1.a1', '30.a1.a1', '30.b1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.d1.a1', '120.s1.a1', '120.s1.b1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3568, 5783, 8607, 9013, 4583, 1336, 8669, 1192], 'generators': [2, 488, 240], 'label': '960.10116.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.b1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1', '120.b1.a1', '120.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '30.1', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319638
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '60.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.b1.b1', '30.a1.a1', '30.b1.b1', '30.d1.b1'], 'contains': ['120.a1.b1', '120.b1.a1', '120.d1.b1', '120.s1.c1', '120.s1.d1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3568, 5783, 8662, 9333, 4583, 1336, 8855, 1078], 'generators': [1, 488, 240], 'label': '960.10116.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.a1.b1', 'normal_contained_in': ['12.a1.b1', '20.b1.b1', '30.a1.a1'], 'normal_contains': ['120.a1.b1', '120.b1.a1', '120.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.b1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '30.1', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '60.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319639
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '60.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.c1.a1', '30.a1.a1', '30.c1.a1', '30.e1.a1'], 'contains': ['120.a1.a1', '120.d1.b1', '120.e1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4159, 8506, 7447, 9176, 5438, 1504, 8101, 1419], 'generators': [241, 2], 'label': '960.10116.60.b1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.b1.a1', 'normal_contained_in': ['12.b1.a1', '20.c1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1', '120.d1.b1', '120.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319640
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '60.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '20.c1.b1', '30.a1.a1', '30.c1.b1', '30.e1.b1'], 'contains': ['120.a1.b1', '120.d1.a1', '120.e1.a1'], 'core': '60.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4159, 8506, 7874, 8714, 5438, 1504, 7761, 1601], 'generators': [1, 242], 'label': '960.10116.60.b1.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.b1.b1', 'normal_contained_in': ['12.b1.b1', '20.c1.b1', '30.a1.a1'], 'normal_contains': ['120.a1.b1', '120.d1.a1', '120.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.b1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319657
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '20.k1.a1', '30.c1.a1', '30.c1.b1', '30.h1.a1'], 'contains': ['120.e1.a1', '120.g1.a1', '120.h1.a1', '120.n1.a1', '120.n1.b1'], 'core': '120.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4387, -1, 7401, -1, 4703, -1, 7121, -1], 'generators': [731, 4, 480], 'label': '960.10116.60.m1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.m1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319641
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '60.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 384, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.g1.a1', '30.a1.a1', '30.f1.a1', '30.g1.a1'], 'contains': ['120.a1.a1', '120.a1.b1', '120.c1.a1', '120.f1.a1', '120.f1.b1', '120.f1.c1', '120.f1.d1'], 'core': '60.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8606, 8946, 4207, 6987, 8371, 401, 5892, 3601], 'generators': [1, 2, 480], 'label': '960.10116.60.c1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.c1.a1', 'normal_contained_in': ['12.c1.a1', '20.g1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.b1', '120.a1.a1', '120.c1.a1', '120.f1.b1', '120.f1.d1', '120.f1.a1', '120.f1.c1'], 'normalizer': '1.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319642
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '60.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.l1.a1', '30.a1.a1', '30.h1.a1', '30.j1.a1'], 'contains': ['120.b1.a1', '120.c1.a1', '120.e1.a1'], 'core': '60.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5668, 8717, 8268, 9101, 6592, 1626, 8202, 982], 'generators': [3, 240], 'label': '960.10116.60.d1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.d1.a1', 'normal_contained_in': ['12.d1.a1', '20.l1.a1', '30.a1.a1'], 'normal_contains': ['120.b1.a1', '120.e1.a1', '120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '120.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '30.1', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319643
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '60.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 384, 'centralizer': '4.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.o1.a1', '30.a1.a1', '30.i1.a1', '30.k1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.d1.b1'], 'core': '60.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8455, 8287, 9098, 8916, 7828, 748, 8397, 1776], 'generators': [241, 242], 'label': '960.10116.60.e1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '60.e1.a1', 'normal_contained_in': ['12.e1.a1', '20.o1.a1', '30.a1.a1'], 'normal_contains': ['120.d1.a1', '120.d1.b1', '120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319644
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '20.a1.a1', '30.b1.a1', '30.c1.a1', '30.f1.a1'], 'contains': ['120.a1.a1', '120.g1.a1', '120.j1.b1', '120.o1.a1', '120.o1.b1', '120.o1.c1', '120.o1.d1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3745, -1, 4563, -1, 5849, -1, 6005, -1], 'generators': [405, 2, 480], 'label': '960.10116.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319645
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.b1', '20.a1.b1', '30.b1.b1', '30.c1.b1', '30.f1.a1'], 'contains': ['120.a1.b1', '120.g1.a1', '120.j1.a1', '120.o1.e1', '120.o1.f1', '120.o1.g1', '120.o1.h1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3745, -1, 4328, -1, 5849, -1, 5787, -1], 'generators': [1, 406, 480], 'label': '960.10116.60.f1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.f1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319646
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '20.d1.a1', '30.c1.a1', '30.d1.a1', '30.g1.a1'], 'contains': ['120.a1.a1', '120.h1.a1', '120.k1.a1', '120.m1.a1', '120.m1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5763, -1, 6879, -1, 5541, -1, 6996, -1], 'generators': [2, 4, 480], 'label': '960.10116.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.g1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319647
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.a1', '2.k1.a1'], 'contains': ['8.e1.a1', '8.g1.a1', '8.i1.a1', '12.s1.a1', '20.s1.a1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5627, 3077, 7689, 5319, 3370, 7581, 5329, 5143], 'generators': [242, 640, 192, 8, 4, 480], 'label': '960.10116.4.s1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.b1.b1', '2.c1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.g1.a1', '8.i1.a1', '20.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319648
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '20.d1.b1', '30.c1.b1', '30.d1.b1', '30.g1.a1'], 'contains': ['120.a1.b1', '120.h1.a1', '120.k1.b1', '120.m1.c1', '120.m1.d1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5763, -1, 5359, -1, 5541, -1, 6935, -1], 'generators': [1, 4, 480], 'label': '960.10116.60.g1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.g1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319649
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '20.e1.a1', '30.d1.a1', '30.e1.a1', '30.f1.a1'], 'contains': ['120.a1.a1', '120.i1.a1', '120.j1.a1', '120.p1.a1', '120.p1.b1', '120.p1.c1', '120.p1.d1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6866, -1, 4679, -1, 6398, -1, 5949, -1], 'generators': [2, 404, 480], 'label': '960.10116.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.h1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319650
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '20.e1.b1', '30.d1.b1', '30.e1.b1', '30.f1.a1'], 'contains': ['120.a1.b1', '120.i1.a1', '120.j1.b1', '120.p1.e1', '120.p1.f1', '120.p1.g1', '120.p1.h1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6866, -1, 4497, -1, 6398, -1, 6250, -1], 'generators': [1, 404, 480], 'label': '960.10116.60.h1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.h1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319651
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '20.f1.a1', '30.b1.a1', '30.e1.a1', '30.g1.a1'], 'contains': ['120.a1.a1', '120.k1.b1', '120.l1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2531, -1, 5890, -1, 5281, -1, 7994, -1], 'generators': [5, 2], 'label': '960.10116.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.i1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319652
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '20.f1.b1', '30.b1.b1', '30.e1.b1', '30.g1.a1'], 'contains': ['120.a1.b1', '120.k1.a1', '120.l1.a1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2531, -1, 7645, -1, 5281, -1, 7717, -1], 'generators': [1, 6], 'label': '960.10116.60.i1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.i1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319653
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '20.h1.a1', '30.b1.a1', '30.b1.b1', '30.h1.a1'], 'contains': ['120.b1.a1', '120.g1.a1', '120.l1.a1', '120.t1.a1', '120.t1.b1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1641, -1, 8318, -1, 3699, -1, 8608, -1], 'generators': [7, 488, 240], 'label': '960.10116.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.j1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319654
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '20.i1.a1', '30.f1.a1', '30.h1.a1', '30.i1.a1'], 'contains': ['120.c1.a1', '120.g1.a1', '120.i1.a1', '120.q1.a1', '120.q1.b1', '120.q1.c1', '120.q1.d1'], 'core': '120.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8723, -1, 4155, -1, 7923, -1, 6190, -1], 'generators': [3, 404, 480], 'label': '960.10116.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.k1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319655
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '20.j1.a1', '30.b1.a1', '30.c1.b1', '30.i1.a1'], 'contains': ['120.d1.a1', '120.g1.a1', '120.k1.b1'], 'core': '120.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3212, -1, 5626, -1, 5195, -1, 7535, -1], 'generators': [5, 242], 'label': '960.10116.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.l1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319656
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '20.j1.b1', '30.b1.b1', '30.c1.a1', '30.i1.a1'], 'contains': ['120.d1.b1', '120.g1.a1', '120.k1.a1'], 'core': '120.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3212, -1, 7065, -1, 5195, -1, 7673, -1], 'generators': [241, 6], 'label': '960.10116.60.l1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.l1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319658
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.b1', '2.k1.a1'], 'contains': ['8.e1.b1', '8.g1.a1', '8.i1.b1', '12.s1.b1', '20.s1.b1'], 'core': '4.s1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5627, 3077, 6819, 5177, 3370, 7581, 6116, 5271], 'generators': [241, 640, 192, 8, 4, 480], 'label': '960.10116.4.s1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.b1', 'normal_contained_in': ['2.b1.a1', '2.c1.b1', '2.k1.a1'], 'normal_contains': ['8.e1.b1', '8.g1.a1', '8.i1.b1', '20.s1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319659
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '20.m1.a1', '30.d1.a1', '30.d1.b1', '30.h1.a1'], 'contains': ['120.b1.a1', '120.h1.a1', '120.i1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5531, -1, 7967, -1, 6119, -1, 8063, -1], 'generators': [4, 240], 'label': '960.10116.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.n1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319660
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '20.n1.a1', '30.b1.b1', '30.d1.a1', '30.j1.a1'], 'contains': ['120.b1.a1', '120.j1.a1', '120.k1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6710, -1, 7839, -1, 5695, -1, 7497, -1], 'generators': [6, 240], 'label': '960.10116.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.o1.a1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319661
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.b1', '20.n1.b1', '30.b1.a1', '30.d1.b1', '30.j1.a1'], 'contains': ['120.b1.a1', '120.j1.b1', '120.k1.b1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6710, -1, 5843, -1, 5695, -1, 8031, -1], 'generators': [5, 240], 'label': '960.10116.60.o1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.n1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.o1.b1', 'projective_image': '120.45', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319662
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '60.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '20.p1.a1', '30.g1.a1', '30.h1.a1', '30.k1.a1'], 'contains': ['120.c1.a1', '120.h1.a1', '120.l1.a1'], 'core': '120.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7947, -1, 8473, -1, 6654, -1, 8170, -1], 'generators': [3, 4], 'label': '960.10116.60.p1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.p1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319663
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 384, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '20.q1.a1', '30.f1.a1', '30.j1.a1', '30.k1.a1'], 'contains': ['120.c1.a1', '120.j1.a1', '120.j1.b1', '120.r1.a1', '120.r1.b1', '120.r1.c1', '120.r1.d1'], 'core': '120.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9083, -1, 4254, -1, 8267, -1, 5839, -1], 'generators': [405, 406, 480], 'label': '960.10116.60.q1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.q1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319664
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.27', 'aut_weyl_index': 384, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '20.r1.a1', '30.g1.a1', '30.i1.a1', '30.j1.a1'], 'contains': ['120.c1.a1', '120.k1.a1', '120.k1.b1'], 'core': '120.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7879, -1, 4880, -1, 8018, -1, 7169, -1], 'generators': [5, 6], 'label': '960.10116.60.r1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.r1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319665
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.a1', '20.s1.a1', '30.c1.b1', '30.d1.a1', '30.k1.a1'], 'contains': ['120.d1.a1', '120.h1.a1', '120.j1.a1'], 'core': '120.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6646, -1, 8417, -1, 6057, -1, 7466, -1], 'generators': [242, 4], 'label': '960.10116.60.s1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.s1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319666
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.s1.b1', '20.s1.b1', '30.c1.a1', '30.d1.b1', '30.k1.a1'], 'contains': ['120.d1.b1', '120.h1.a1', '120.j1.b1'], 'core': '120.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6646, -1, 7525, -1, 6057, -1, 7924, -1], 'generators': [241, 4], 'label': '960.10116.60.s1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.s1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.s1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319667
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '20.t1.a1', '30.d1.a1', '30.e1.b1', '30.i1.a1'], 'contains': ['120.d1.a1', '120.i1.a1', '120.k1.a1'], 'core': '120.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6199, -1, 7611, -1, 6307, -1, 7573, -1], 'generators': [242, 404], 'label': '960.10116.60.t1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.t1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319668
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.b1', '20.t1.b1', '30.d1.b1', '30.e1.a1', '30.i1.a1'], 'contains': ['120.d1.b1', '120.i1.a1', '120.k1.b1'], 'core': '120.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6199, -1, 5812, -1, 6307, -1, 7956, -1], 'generators': [241, 404], 'label': '960.10116.60.t1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.t1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.t1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.t1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319669
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.t1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.i1.a1'], 'contains': ['8.e1.a1', '8.h1.a1', '8.j1.a1', '12.t1.a1', '20.t1.a1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5474, 4009, 7129, 6732, 3665, 6158, 5543, 3615], 'generators': [242, 640, 192, 488, 404, 480], 'label': '960.10116.4.t1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.i1.a1'], 'normal_contains': ['8.e1.a1', '8.h1.a1', '8.j1.a1', '20.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319670
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '20.u1.a1', '30.b1.a1', '30.e1.b1', '30.k1.a1'], 'contains': ['120.d1.a1', '120.j1.b1', '120.l1.a1'], 'core': '120.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2419, -1, 8387, -1, 5360, -1, 8235, -1], 'generators': [405, 242], 'label': '960.10116.60.u1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.u1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319671
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.b1', '20.u1.b1', '30.b1.b1', '30.e1.a1', '30.k1.a1'], 'contains': ['120.d1.b1', '120.j1.a1', '120.l1.a1'], 'core': '120.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2419, -1, 8516, -1, 5360, -1, 8496, -1], 'generators': [241, 406], 'label': '960.10116.60.u1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.u1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.u1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.u1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319672
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '60.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '20.v1.a1', '30.e1.a1', '30.e1.b1', '30.h1.a1'], 'contains': ['120.e1.a1', '120.i1.a1', '120.l1.a1'], 'core': '120.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3473, -1, 7921, -1, 5633, -1, 8139, -1], 'generators': [731, 404], 'label': '960.10116.60.v1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.v1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319673
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '20.w1.a1', '30.c1.b1', '30.e1.a1', '30.j1.a1'], 'contains': ['120.e1.a1', '120.j1.a1', '120.k1.b1'], 'core': '120.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4948, -1, 5772, -1, 5761, -1, 7269, -1], 'generators': [645, 406], 'label': '960.10116.60.w1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.w1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319674
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '60.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.14', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.b1', '20.w1.b1', '30.c1.a1', '30.e1.b1', '30.j1.a1'], 'contains': ['120.e1.a1', '120.j1.b1', '120.k1.a1'], 'core': '120.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4948, -1, 7147, -1, 5761, -1, 7305, -1], 'generators': [725, 6], 'label': '960.10116.60.w1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.w1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.w1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319675
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.a1', '20.x1.a1', '30.f1.a1'], 'contains': ['120.f1.a1', '120.o1.a1', '120.o1.e1', '120.p1.a1', '120.p1.e1', '120.q1.a1', '120.r1.a1'], 'core': '120.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 1156, -1, 8929, -1, 2857, -1], 'generators': [1, 2, 404], 'label': '960.10116.60.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319676
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.b1', '20.x1.b1', '30.f1.a1'], 'contains': ['120.f1.a1', '120.o1.b1', '120.o1.f1', '120.p1.b1', '120.p1.f1', '120.q1.c1', '120.r1.b1'], 'core': '120.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 3182, -1, 8929, -1, 2633, -1], 'generators': [1, 2, 884], 'label': '960.10116.60.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319677
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.c1', '20.x1.c1', '30.f1.a1'], 'contains': ['120.f1.b1', '120.o1.a1', '120.o1.g1', '120.p1.b1', '120.p1.h1', '120.q1.b1', '120.r1.d1'], 'core': '120.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 2371, -1, 8929, -1, 3353, -1], 'generators': [481, 2, 884], 'label': '960.10116.60.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319678
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.d1', '20.x1.d1', '30.f1.a1'], 'contains': ['120.f1.b1', '120.o1.b1', '120.o1.h1', '120.p1.a1', '120.p1.g1', '120.q1.d1', '120.r1.c1'], 'core': '120.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 3394, -1, 8929, -1, 3993, -1], 'generators': [481, 2, 404], 'label': '960.10116.60.x1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319679
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.e1', '20.x1.e1', '30.f1.a1'], 'contains': ['120.f1.c1', '120.o1.c1', '120.o1.e1', '120.p1.d1', '120.p1.f1', '120.q1.b1', '120.r1.c1'], 'core': '120.f1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 3664, -1, 8929, -1, 3528, -1], 'generators': [1, 482, 884], 'label': '960.10116.60.x1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.e1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319680
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.t1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '2.d1.a1', '2.i1.a1'], 'contains': ['8.e1.b1', '8.h1.a1', '8.j1.b1', '12.t1.b1', '20.t1.b1'], 'core': '4.t1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5474, 4009, 5451, 7751, 3665, 6158, 6191, 2565], 'generators': [241, 640, 192, 488, 404, 480], 'label': '960.10116.4.t1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.b1', 'normal_contained_in': ['2.c1.b1', '2.d1.a1', '2.i1.a1'], 'normal_contains': ['8.e1.b1', '8.h1.a1', '8.j1.b1', '20.t1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319681
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.f1', '20.x1.f1', '30.f1.a1'], 'contains': ['120.f1.c1', '120.o1.d1', '120.o1.f1', '120.p1.c1', '120.p1.e1', '120.q1.d1', '120.r1.d1'], 'core': '120.f1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 1721, -1, 8929, -1, 3493, -1], 'generators': [1, 482, 404], 'label': '960.10116.60.x1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.f1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319682
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.g1', '20.x1.g1', '30.f1.a1'], 'contains': ['120.f1.d1', '120.o1.c1', '120.o1.g1', '120.p1.c1', '120.p1.g1', '120.q1.a1', '120.r1.b1'], 'core': '120.f1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 3817, -1, 8929, -1, 3958, -1], 'generators': [481, 482, 404], 'label': '960.10116.60.x1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.g1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319683
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '60.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 768, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.x1.h1', '20.x1.h1', '30.f1.a1'], 'contains': ['120.f1.d1', '120.o1.d1', '120.o1.h1', '120.p1.d1', '120.p1.h1', '120.q1.c1', '120.r1.a1'], 'core': '120.f1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [9619, -1, 1286, -1, 8929, -1, 2497, -1], 'generators': [481, 482, 884], 'label': '960.10116.60.x1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.x1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '60.x1.h1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.x1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319684
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '64.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1536, 'centralizer': '2.f1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.d1.b1', '32.d1.c1', '32.d1.d1', '32.e1.a1', '32.e1.b1'], 'contains': ['192.a1.a1', '320.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2107, 5103, 5312, 4512, 2258, 3348, 4461, 3661], 'generators': [640, 192], 'label': '960.10116.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.c1.a1', '32.a1.a1', '32.b1.a1'], 'normal_contains': ['192.a1.a1', '320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '192.1095', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.25', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319685
    {'ambient': '960.10116', 'aut_centralizer_order': 6144, 'aut_label': '80.a1', 'aut_quo_index': 10080, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.a1.b1', '40.b1.a1', '40.c1.a1', '40.d1.a1', '40.e1.a1', '40.e1.b1', '40.f1.a1', '40.g1.a1', '40.h1.a1', '40.i1.a1', '40.i1.b1', '40.j1.a1', '40.j1.b1', '40.k1.a1'], 'contains': ['160.a1.a1', '160.b1.a1', '160.c1.a1', '240.a1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4071, 4086, 5540, 6378, 2846, 4509, 6610, 3502], 'generators': [488, 480, 640], 'label': '960.10116.80.a1.a1', 'mobius_quo': -2, 'mobius_sub': -64, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.b1', '40.a1.a1', '40.b1.a1', '40.c1.a1', '40.e1.a1', '40.e1.b1', '40.f1.a1', '40.d1.a1', '40.h1.a1', '40.g1.a1', '40.i1.a1', '40.i1.b1', '40.j1.a1', '40.j1.b1', '40.k1.a1'], 'normal_contains': ['160.c1.a1', '160.a1.a1', '160.b1.a1', '240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.14', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319686
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': ['12.x1.a1', '12.x1.d1', '12.x1.f1', '12.x1.g1', '12.x1.b1', '12.x1.c1', '12.x1.e1', '12.x1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '40.g1.a1', '40.q1.a1', '40.q1.c1', '40.r1.a1'], 'contains': ['160.a1.a1', '240.h1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4777, 2259, 6448, 4712, 2622, 8623, 5141, 3638], 'generators': [4, 8, 640], 'label': '960.10116.80.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.b1.a1', 'normal_contained_in': ['16.b1.a1', '40.g1.a1'], 'normal_contains': ['160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '480.1160', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.10', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319687
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.b1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': ['12.x1.b1', '12.x1.c1', '12.x1.e1', '12.x1.h1', '12.x1.a1', '12.x1.d1', '12.x1.f1', '12.x1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '40.g1.a1', '40.q1.b1', '40.q1.d1', '40.r1.b1'], 'contains': ['160.a1.a1', '240.h1.b1'], 'core': '80.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4777, 2259, 6678, 4809, 2622, 8623, 5292, 3578], 'generators': [484, 8, 640], 'label': '960.10116.80.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.b1.b1', 'normal_contained_in': ['16.b1.b1', '40.g1.a1'], 'normal_contains': ['160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.b1.b1', 'projective_image': '480.1160', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.10', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319688
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '40.a1.a1', '40.l1.a1', '40.l1.b1', '40.m1.a1', '40.m1.b1', '40.n1.a1', '40.n1.b1'], 'contains': ['160.b1.a1', '160.d1.a1', '240.b1.a1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7777, 7543, 2314, 1292, 6870, 2853, 3299, 6082], 'generators': [2, 488, 640], 'label': '960.10116.80.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1.a1', 'normal_contained_in': ['16.c1.a1', '40.a1.a1', '40.l1.a1', '40.l1.b1', '40.m1.b1', '40.m1.a1', '40.n1.b1', '40.n1.a1'], 'normal_contains': ['160.b1.a1', '240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.c1.a1', 'projective_image': '480.1151', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319689
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '40.a1.a1', '40.l1.c1', '40.l1.d1', '40.m1.c1', '40.m1.d1', '40.n1.c1', '40.n1.d1'], 'contains': ['160.b1.a1', '160.d1.b1', '240.b1.b1'], 'core': '80.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7777, 7543, 2921, 2558, 6870, 2853, 3467, 5692], 'generators': [482, 488, 640], 'label': '960.10116.80.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1.b1', 'normal_contained_in': ['16.c1.b1', '40.a1.a1', '40.l1.c1', '40.l1.d1', '40.m1.d1', '40.m1.c1', '40.n1.d1', '40.n1.c1'], 'normal_contains': ['160.b1.a1', '240.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '80.c1.b1', 'projective_image': '480.1151', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319690
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.c1', '40.a1.b1', '40.l1.e1', '40.l1.f1', '40.m1.e1', '40.m1.f1', '40.n1.a1', '40.n1.c1'], 'contains': ['160.b1.a1', '160.d1.c1', '240.b1.c1'], 'core': '80.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7777, 7543, 2183, 3073, 6870, 2853, 3100, 5781], 'generators': [1, 488, 640], 'label': '960.10116.80.c1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1.c1', 'normal_contained_in': ['16.c1.c1', '40.a1.b1', '40.l1.e1', '40.l1.f1', '40.m1.f1', '40.m1.e1', '40.n1.a1', '40.n1.c1'], 'normal_contains': ['160.b1.a1', '240.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '80.c1.c1', 'projective_image': '480.1151', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.c1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319691
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.u1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.b1', '2.k1.a1'], 'contains': ['8.e1.a1', '8.i1.b1', '8.k1.a1', '12.u1.a1', '20.u1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1832, 3355, 7626, 6214, 2015, 5726, 7585, 1858], 'generators': [405, 640, 192, 488, 242, 480], 'label': '960.10116.4.u1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.b1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.i1.b1', '8.k1.a1', '20.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319692
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.c1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.d1', '40.a1.b1', '40.l1.g1', '40.l1.h1', '40.m1.g1', '40.m1.h1', '40.n1.b1', '40.n1.d1'], 'contains': ['160.b1.a1', '160.d1.d1', '240.b1.d1'], 'core': '80.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7777, 7543, 3096, 791, 6870, 2853, 3680, 5992], 'generators': [481, 488, 640], 'label': '960.10116.80.c1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1.d1', 'normal_contained_in': ['16.c1.d1', '40.a1.b1', '40.l1.g1', '40.l1.h1', '40.m1.h1', '40.m1.g1', '40.n1.b1', '40.n1.d1'], 'normal_contains': ['160.b1.a1', '240.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '80.c1.d1', 'projective_image': '480.1151', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.c1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319693
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '40.b1.a1', '40.l1.a1', '40.l1.c1', '40.l1.e1', '40.l1.g1', '40.o1.a1', '40.o1.b1'], 'contains': ['160.b1.a1', '160.e1.a1', '240.j1.a1'], 'core': '80.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6403, 6339, 2668, 991, 6599, 3207, 3560, 6150], 'generators': [407, 488, 640], 'label': '960.10116.80.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.d1.a1', 'normal_contained_in': ['16.d1.a1', '40.b1.a1', '40.l1.g1', '40.l1.a1', '40.l1.c1', '40.l1.e1', '40.o1.b1', '40.o1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.d1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319694
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '40.b1.a1', '40.l1.b1', '40.l1.d1', '40.l1.f1', '40.l1.h1', '40.o1.c1', '40.o1.d1'], 'contains': ['160.b1.a1', '160.e1.b1', '240.j1.b1'], 'core': '80.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6403, 6339, 2513, 4003, 6599, 3207, 2952, 6661], 'generators': [887, 488, 640], 'label': '960.10116.80.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.d1.b1', 'normal_contained_in': ['16.d1.b1', '40.b1.a1', '40.l1.h1', '40.l1.b1', '40.l1.d1', '40.l1.f1', '40.o1.d1', '40.o1.c1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.d1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319695
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '80.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '40.d1.a1', '40.n1.a1', '40.n1.d1', '40.o1.a1', '40.o1.c1', '40.p1.a1', '40.p1.b1'], 'contains': ['160.b1.a1', '240.c1.a1'], 'core': '80.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9403, 7775, 1928, 1460, 8541, 2713, 2708, 5422], 'generators': [3, 640, 488], 'label': '960.10116.80.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.e1.a1', 'normal_contained_in': ['16.e1.a1', '40.d1.a1', '40.n1.d1', '40.n1.a1', '40.o1.a1', '40.o1.c1', '40.p1.a1', '40.p1.b1'], 'normal_contains': ['160.b1.a1', '240.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.e1.a1', 'projective_image': '480.1151', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319696
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '80.e1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '40.d1.a1', '40.n1.b1', '40.n1.c1', '40.o1.b1', '40.o1.d1', '40.p1.c1', '40.p1.d1'], 'contains': ['160.b1.a1', '240.c1.b1'], 'core': '80.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9403, 7775, 3264, 2476, 8541, 2713, 3759, 6203], 'generators': [483, 640, 488], 'label': '960.10116.80.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.e1.b1', 'normal_contained_in': ['16.e1.b1', '40.d1.a1', '40.n1.b1', '40.n1.c1', '40.o1.b1', '40.o1.d1', '40.p1.c1', '40.p1.d1'], 'normal_contains': ['160.b1.a1', '240.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '80.e1.b1', 'projective_image': '480.1151', 'quotient_action_image': '4.2', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '80.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319697
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.f1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '40.h1.a1', '40.m1.a1', '40.m1.c1', '40.m1.e1', '40.m1.g1', '40.o1.a1', '40.o1.d1'], 'contains': ['160.b1.a1', '240.k1.a1'], 'core': '80.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8257, 7290, 2101, 3157, 7207, 3309, 3849, 5857], 'generators': [404, 488, 640], 'label': '960.10116.80.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.f1.a1', 'normal_contained_in': ['16.f1.a1', '40.h1.a1', '40.m1.g1', '40.m1.a1', '40.m1.c1', '40.m1.e1', '40.o1.a1', '40.o1.d1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.f1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319698
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.f1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '40.h1.a1', '40.m1.b1', '40.m1.d1', '40.m1.f1', '40.m1.h1', '40.o1.b1', '40.o1.c1'], 'contains': ['160.b1.a1', '240.k1.b1'], 'core': '80.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8257, 7290, 2697, 1988, 7207, 3309, 2638, 6732], 'generators': [884, 488, 640], 'label': '960.10116.80.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.f1.b1', 'normal_contained_in': ['16.f1.b1', '40.h1.a1', '40.m1.h1', '40.m1.b1', '40.m1.d1', '40.m1.f1', '40.o1.b1', '40.o1.c1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.f1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319699
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '80.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '40.i1.a1', '40.l1.e1', '40.l1.h1', '40.m1.a1', '40.m1.d1', '40.p1.a1', '40.p1.c1'], 'contains': ['160.b1.a1', '240.l1.a1'], 'core': '80.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7378, 6807, 1999, 1710, 7137, 3105, 3172, 6793], 'generators': [406, 488, 640], 'label': '960.10116.80.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.g1.a1', 'normal_contained_in': ['16.g1.a1', '40.i1.a1', '40.l1.h1', '40.l1.e1', '40.m1.a1', '40.m1.d1', '40.p1.c1', '40.p1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.g1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319700
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '80.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '40.i1.b1', '40.l1.a1', '40.l1.d1', '40.m1.e1', '40.m1.h1', '40.p1.a1', '40.p1.d1'], 'contains': ['160.b1.a1', '240.l1.b1'], 'core': '80.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7378, 6807, 1557, 3353, 7137, 3105, 2674, 7084], 'generators': [405, 488, 640], 'label': '960.10116.80.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.g1.b1', 'normal_contained_in': ['16.g1.b1', '40.i1.b1', '40.l1.a1', '40.l1.d1', '40.m1.h1', '40.m1.e1', '40.p1.d1', '40.p1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.g1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319701
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '80.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.c1', '40.i1.a1', '40.l1.f1', '40.l1.g1', '40.m1.b1', '40.m1.c1', '40.p1.b1', '40.p1.d1'], 'contains': ['160.b1.a1', '240.l1.c1'], 'core': '80.g1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7378, 6807, 2960, 2991, 7137, 3105, 3343, 5917], 'generators': [886, 488, 640], 'label': '960.10116.80.g1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.g1.c1', 'normal_contained_in': ['16.g1.c1', '40.i1.a1', '40.l1.g1', '40.l1.f1', '40.m1.b1', '40.m1.c1', '40.p1.d1', '40.p1.b1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.g1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319702
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.u1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.d1.a1', '2.k1.a1'], 'contains': ['8.e1.b1', '8.i1.a1', '8.k1.a1', '12.u1.b1', '20.u1.b1'], 'core': '4.u1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1832, 3355, 7836, 6601, 2015, 5726, 8026, 1748], 'generators': [241, 640, 192, 488, 406, 480], 'label': '960.10116.4.u1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.b1', 'normal_contained_in': ['2.a1.b1', '2.d1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.b1', '8.i1.a1', '8.k1.a1', '20.u1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319703
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '80.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.d1', '40.i1.b1', '40.l1.b1', '40.l1.c1', '40.m1.f1', '40.m1.g1', '40.p1.b1', '40.p1.c1'], 'contains': ['160.b1.a1', '240.l1.d1'], 'core': '80.g1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7378, 6807, 3522, 2266, 7137, 3105, 3724, 5617], 'generators': [885, 488, 640], 'label': '960.10116.80.g1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.g1.d1', 'normal_contained_in': ['16.g1.d1', '40.i1.b1', '40.l1.b1', '40.l1.c1', '40.m1.g1', '40.m1.f1', '40.p1.c1', '40.p1.b1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.g1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319704
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '80.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.f1.a1', 'complements': ['12.x1.a1', '12.x1.d1', '12.x1.f1', '12.x1.g1', '12.x1.b1', '12.x1.c1', '12.x1.e1', '12.x1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '40.c1.a1', '40.s1.a1', '40.s1.c1', '40.t1.a1'], 'contains': ['160.c1.a1', '240.d1.a1'], 'core': '80.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [968, 2061, 9618, 8591, 1015, 3421, 9523, 1944], 'generators': [240, 640, 480], 'label': '960.10116.80.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.h1.a1', 'normal_contained_in': ['16.h1.a1', '40.c1.a1'], 'normal_contains': ['160.c1.a1', '240.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.h1.a1', 'projective_image': '240.170', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.10', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319705
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '80.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.f1.a1', 'complements': ['12.x1.b1', '12.x1.c1', '12.x1.e1', '12.x1.h1', '12.x1.a1', '12.x1.d1', '12.x1.f1', '12.x1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '40.c1.a1', '40.s1.b1', '40.s1.d1', '40.t1.b1'], 'contains': ['160.c1.a1', '240.d1.b1'], 'core': '80.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [968, 2061, 9746, 8443, 1015, 3421, 9350, 1878], 'generators': [728, 640, 480], 'label': '960.10116.80.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.h1.b1', 'normal_contained_in': ['16.h1.b1', '40.c1.a1'], 'normal_contains': ['160.c1.a1', '240.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '80.h1.b1', 'projective_image': '240.170', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.10', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319706
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '40.a1.a1', '40.q1.a1', '40.q1.b1'], 'contains': ['160.a1.a1', '160.d1.a1', '160.d1.b1', '240.e1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3462, -1, 6128, -1, 2535, -1, 5045, -1], 'generators': [2, 8, 640], 'label': '960.10116.80.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '80.i1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319707
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '40.a1.b1', '40.q1.c1', '40.q1.d1'], 'contains': ['160.a1.a1', '160.d1.c1', '160.d1.d1', '240.e1.b1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3462, -1, 4513, -1, 2535, -1, 4871, -1], 'generators': [1, 8, 640], 'label': '960.10116.80.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '80.i1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319708
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '40.b1.a1', '40.r1.a1', '40.r1.b1'], 'contains': ['160.a1.a1', '160.e1.a1', '160.e1.b1', '240.f1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1524, -1, 6934, -1, 2197, -1, 5209, -1], 'generators': [407, 8, 640], 'label': '960.10116.80.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '80.j1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319709
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '80.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '40.f1.a1', '40.r1.a1', '40.r1.b1'], 'contains': ['160.a1.a1', '240.g1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2167, -1, 7252, -1, 2450, -1, 5432, -1], 'generators': [731, 640, 8], 'label': '960.10116.80.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '80.k1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319710
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '80.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '40.j1.a1', '40.q1.a1', '40.q1.b1'], 'contains': ['160.a1.a1', '240.i1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4695, -1, 6337, -1, 2692, -1, 5177, -1], 'generators': [6, 8, 640], 'label': '960.10116.80.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '80.l1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319711
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '80.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.b1', '40.j1.b1', '40.q1.c1', '40.q1.d1'], 'contains': ['160.a1.a1', '240.i1.b1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4695, -1, 4658, -1, 2692, -1, 5001, -1], 'generators': [5, 8, 640], 'label': '960.10116.80.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '80.l1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319712
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '40.a1.a1', '40.s1.a1', '40.s1.b1'], 'contains': ['160.c1.a1', '160.d1.a1', '160.d1.b1', '240.m1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1397, -1, 9258, -1, 1823, -1, 8978, -1], 'generators': [2, 480, 640], 'label': '960.10116.80.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '80.m1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319713
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['480.d1.a1', '480.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.c1.b1', '4.d1.b1', '4.j1.a1', '4.k1.a1', '4.s1.a1', '4.w1.a1', '6.c1.b1', '10.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3636, 3717, 5544, 4937, 2995, 6657, 5074, 4533], 'generators': [1, 480, 4, 192, 242, 640, 488], 'label': '960.10116.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.c1.b1', '4.d1.b1', '4.j1.a1', '4.k1.a1', '4.s1.a1', '4.w1.a1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319714
    {'ambient': '960.10116', 'aut_centralizer_order': 32, 'aut_label': '4.v1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.d1.b1', '2.h1.a1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.k1.a1', '12.v1.a1', '20.v1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2269, 6045, 7284, 6347, 2649, 7823, 6903, 1473], 'generators': [731, 640, 192, 8, 404, 480], 'label': '960.10116.4.v1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.d1.b1', '2.d1.a1', '2.h1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.k1.a1', '20.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319715
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '40.a1.b1', '40.s1.c1', '40.s1.d1'], 'contains': ['160.c1.a1', '160.d1.c1', '160.d1.d1', '240.m1.b1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1397, -1, 9842, -1, 1823, -1, 9238, -1], 'generators': [1, 480, 640], 'label': '960.10116.80.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '80.m1.b1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319716
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '40.b1.a1', '40.t1.a1', '40.t1.b1'], 'contains': ['160.c1.a1', '160.e1.a1', '160.e1.b1', '240.n1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [801, -1, 9666, -1, 1247, -1, 8702, -1], 'generators': [407, 480, 640], 'label': '960.10116.80.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '80.n1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319717
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '40.e1.a1', '40.s1.a1', '40.s1.b1'], 'contains': ['160.c1.a1', '240.o1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1278, -1, 9535, -1, 1567, -1, 9316, -1], 'generators': [242, 640, 480], 'label': '960.10116.80.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '80.o1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319718
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '80.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.b1', '40.e1.b1', '40.s1.c1', '40.s1.d1'], 'contains': ['160.c1.a1', '240.o1.b1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1278, -1, 9915, -1, 1567, -1, 9690, -1], 'generators': [241, 640, 480], 'label': '960.10116.80.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '80.o1.b1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319719
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '80.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1024, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '40.k1.a1', '40.t1.a1', '40.t1.b1'], 'contains': ['160.c1.a1', '240.p1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [867, -1, 9790, -1, 946, -1, 9282, -1], 'generators': [7, 480, 640], 'label': '960.10116.80.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '80.p1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319720
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '96.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.e1.a1', '48.e1.b1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.h1.b1', '48.i1.a1', '48.i1.b1'], 'contains': ['192.a1.a1', '480.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2869, 5626, 5941, 6869, 2841, 3238, 4793, 3555], 'generators': [8, 192], 'label': '960.10116.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.215', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.215', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319721
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '96.b1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1', '48.b1.d1', '48.c1.a1', '48.c1.b1', '48.j1.a1', '48.j1.b1', '48.k1.a1', '48.k1.b1', '48.l1.a1', '48.l1.b1', '48.l1.c1', '48.l1.d1'], 'contains': ['192.a1.a1', '480.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7477, 7285, 900, 4175, 6919, 1755, 1886, 4882], 'generators': [488, 192], 'label': '960.10116.96.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.b1.a1', '48.a1.a1', '48.b1.d1', '48.b1.a1', '48.b1.b1', '48.b1.c1', '48.c1.b1', '48.c1.a1'], 'normal_contains': ['192.a1.a1', '480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.206', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319722
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '96.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.a1', '48.d1.a1', '48.d1.b1', '48.m1.a1', '48.m1.b1', '48.n1.a1', '48.o1.a1', '48.o1.b1', '48.p1.a1'], 'contains': ['192.a1.a1', '480.c1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [515, 4965, 9054, 9448, 1603, 2772, 8872, 2981], 'generators': [480, 192], 'label': '960.10116.96.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['32.c1.a1', '48.a1.a1', '48.d1.b1', '48.d1.a1'], 'normal_contains': ['192.a1.a1', '480.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '96.210', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.210', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319723
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.b1.a1', '48.e1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '480.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2479, -1, 5382, -1, 2585, -1, 4512, -1], 'generators': [2, 192], 'label': '960.10116.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.d1.a1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319724
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.b1.b1', '48.e1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '480.d1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2479, -1, 5202, -1, 2585, -1, 4614, -1], 'generators': [482, 192], 'label': '960.10116.96.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.d1.b1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319725
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.w1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.d1.a1', '2.j1.a1'], 'contains': ['8.f1.a1', '8.i1.a1', '8.j1.b1', '12.w1.a1', '20.w1.a1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3595, 4347, 5211, 7295, 2934, 5934, 5006, 2319], 'generators': [5, 640, 192, 8, 406, 480], 'label': '960.10116.4.w1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.b1.b1', '2.d1.a1', '2.j1.a1'], 'normal_contains': ['8.f1.a1', '8.i1.a1', '8.j1.b1', '20.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319726
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '48.b1.c1', '48.e1.b1', '48.m1.b1'], 'contains': ['192.a1.a1', '480.d1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2479, -1, 4203, -1, 2585, -1, 4420, -1], 'generators': [1, 192], 'label': '960.10116.96.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '96.d1.c1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319727
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '48.b1.d1', '48.e1.b1', '48.m1.b1'], 'contains': ['192.a1.a1', '480.d1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2479, -1, 4145, -1, 2585, -1, 4546, -1], 'generators': [481, 192], 'label': '960.10116.96.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '96.d1.d1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319728
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.f1.a1', '48.j1.a1', '48.n1.a1'], 'contains': ['192.a1.a1', '480.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [283, -1, 6459, -1, 2364, -1, 4648, -1], 'generators': [407, 192], 'label': '960.10116.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.e1.a1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319729
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '48.f1.a1', '48.j1.b1', '48.n1.a1'], 'contains': ['192.a1.a1', '480.e1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [283, -1, 6537, -1, 2364, -1, 4580, -1], 'generators': [887, 192], 'label': '960.10116.96.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '96.e1.b1', 'projective_image': '192.1095', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319730
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '120.a1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1', '60.f1.a1', '60.g1.a1', '60.h1.a1', '60.i1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.b1.b1', '240.e1.a1', '240.m1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3921, 6483, 5112, 8409, 5281, 1412, 6488, 3362], 'generators': [2, 488, 480], 'label': '960.10116.120.a1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1'], 'normal_contains': ['240.a1.a1', '240.b1.a1', '240.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319731
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '120.a1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '40.a1.b1', '60.a1.b1', '60.b1.b1', '60.c1.a1', '60.f1.b1', '60.g1.b1', '60.h1.b1', '60.i1.b1'], 'contains': ['240.a1.a1', '240.b1.c1', '240.b1.d1', '240.e1.b1', '240.m1.b1'], 'core': '120.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3921, 6483, 4684, 7862, 5281, 1412, 6312, 3184], 'generators': [1, 488, 480], 'label': '960.10116.120.a1.b1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.a1.b1', 'normal_contained_in': ['24.a1.b1', '40.a1.b1', '60.a1.b1', '60.b1.b1', '60.c1.a1'], 'normal_contains': ['240.a1.a1', '240.b1.d1', '240.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.b1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319732
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '120.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.c1.a1', '60.a1.a1', '60.a1.b1', '60.d1.a1', '60.j1.a1', '60.n1.a1', '60.o1.a1', '60.o1.b1'], 'contains': ['240.a1.a1', '240.d1.a1', '240.d1.b1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3651, 5276, 8293, 8999, 4602, 1922, 8414, 1462], 'generators': [488, 240], 'label': '960.10116.120.b1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.b1.a1', 'normal_contained_in': ['24.b1.a1', '40.c1.a1', '60.a1.b1', '60.a1.a1', '60.d1.a1'], 'normal_contains': ['240.a1.a1', '240.d1.b1', '240.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '120.45', 'quotient_action_image': '1.1', 'quotient_action_kernel': '120.45', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319733
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '120.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.d1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1', '60.k1.a1', '60.p1.a1', '60.q1.a1', '60.r1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.c1.b1'], 'core': '120.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8459, 8817, 4369, 8489, 7923, 1276, 6234, 3267], 'generators': [3, 480], 'label': '960.10116.120.c1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.c1.a1', 'normal_contained_in': ['24.c1.a1', '40.d1.a1', '60.c1.a1', '60.d1.a1', '60.e1.a1'], 'normal_contains': ['240.a1.a1', '240.c1.b1', '240.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319734
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '120.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '40.e1.a1', '60.a1.a1', '60.b1.b1', '60.e1.a1', '60.l1.a1', '60.s1.a1', '60.t1.a1', '60.u1.a1'], 'contains': ['240.a1.a1', '240.o1.a1'], 'core': '120.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3324, 7256, 8510, 8891, 5095, 1548, 7761, 1788], 'generators': [242, 488], 'label': '960.10116.120.d1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.d1.a1', 'normal_contained_in': ['24.d1.a1', '40.e1.a1', '60.a1.a1', '60.b1.b1', '60.e1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.d1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319735
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '120.d1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '40.e1.b1', '60.a1.b1', '60.b1.a1', '60.e1.a1', '60.l1.b1', '60.s1.b1', '60.t1.b1', '60.u1.b1'], 'contains': ['240.a1.a1', '240.o1.b1'], 'core': '120.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3324, 7256, 7735, 9098, 5095, 1548, 8101, 1698], 'generators': [241, 488], 'label': '960.10116.120.d1.b1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.d1.b1', 'normal_contained_in': ['24.d1.b1', '40.e1.b1', '60.a1.b1', '60.b1.a1', '60.e1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.d1.b1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319736
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '4.w1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '384.20129', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.j1.a1'], 'contains': ['8.f1.a1', '8.i1.b1', '8.j1.a1', '12.w1.b1', '20.w1.b1'], 'core': '4.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3595, 4347, 6391, 7051, 2934, 5934, 4942, 3496], 'generators': [405, 640, 192, 488, 6, 480], 'label': '960.10116.4.w1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.j1.a1'], 'normal_contains': ['8.f1.a1', '8.i1.b1', '8.j1.a1', '20.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319737
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '120.e1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '40.f1.a1', '60.b1.a1', '60.b1.b1', '60.d1.a1', '60.m1.a1', '60.v1.a1', '60.w1.a1', '60.w1.b1'], 'contains': ['240.a1.a1', '240.g1.a1'], 'core': '120.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4290, 8574, 7389, 8784, 5198, 2091, 7322, 1609], 'generators': [731, 480], 'label': '960.10116.120.e1.a1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '120.e1.a1', 'normal_contained_in': ['24.e1.a1', '40.f1.a1', '60.b1.b1', '60.b1.a1', '60.d1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.e1.a1', 'projective_image': '240.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319738
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '4.m1.a1', 'complements': ['8.t1.a1', '8.t1.b1', '8.r1.a1', '8.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '40.n1.a1', '60.c1.a1', '60.x1.a1', '60.x1.b1'], 'contains': ['240.b1.a1', '240.b1.c1', '240.c1.a1'], 'core': '120.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9410, 8986, 1948, 4323, 8817, 833, 2606, 4655], 'generators': [1, 2], 'label': '960.10116.120.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.f1.a1', 'normal_contained_in': ['24.f1.a1', '40.n1.a1', '60.c1.a1'], 'normal_contains': ['240.b1.a1', '240.b1.c1', '240.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.f1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.4', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319739
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '4.m1.a1', 'complements': ['8.t1.a1', '8.t1.b1', '8.r1.a1', '8.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '40.n1.b1', '60.c1.a1', '60.x1.c1', '60.x1.d1'], 'contains': ['240.b1.a1', '240.b1.d1', '240.c1.b1'], 'core': '120.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9410, 8986, 3098, 3738, 8817, 833, 3817, 5238], 'generators': [481, 2], 'label': '960.10116.120.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.f1.b1', 'normal_contained_in': ['24.f1.b1', '40.n1.b1', '60.c1.a1'], 'normal_contains': ['240.b1.d1', '240.b1.a1', '240.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '120.f1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.4', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319740
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '4.m1.a1', 'complements': ['8.t1.a1', '8.t1.b1', '8.r1.a1', '8.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.c1', '40.n1.c1', '60.c1.a1', '60.x1.e1', '60.x1.f1'], 'contains': ['240.b1.b1', '240.b1.c1', '240.c1.b1'], 'core': '120.f1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9410, 8986, 3035, 4775, 8817, 833, 3587, 4811], 'generators': [1, 482], 'label': '960.10116.120.f1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.f1.c1', 'normal_contained_in': ['24.f1.c1', '40.n1.c1', '60.c1.a1'], 'normal_contains': ['240.b1.b1', '240.b1.c1', '240.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '120.f1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.4', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.f1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319741
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '4.m1.a1', 'complements': ['8.t1.a1', '8.t1.b1', '8.r1.a1', '8.r1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.d1', '40.n1.d1', '60.c1.a1', '60.x1.g1', '60.x1.h1'], 'contains': ['240.b1.b1', '240.b1.d1', '240.c1.a1'], 'core': '120.f1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9410, 8986, 3342, 4004, 8817, 833, 3203, 4608], 'generators': [481, 482], 'label': '960.10116.120.f1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.f1.d1', 'normal_contained_in': ['24.f1.d1', '40.n1.d1', '60.c1.a1'], 'normal_contains': ['240.b1.d1', '240.b1.b1', '240.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.f1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '60.4', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '120.f1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319742
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '40.b1.a1', '60.f1.a1', '60.f1.b1', '60.j1.a1', '60.k1.a1', '60.l1.a1', '60.l1.b1', '60.m1.a1'], 'contains': ['240.a1.a1', '240.f1.a1', '240.j1.a1', '240.j1.b1', '240.n1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3079, -1, 4777, -1, 4703, -1, 6279, -1], 'generators': [407, 488, 480], 'label': '960.10116.120.g1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.g1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319743
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '40.g1.a1', '60.g1.a1', '60.g1.b1', '60.m1.a1', '60.n1.a1', '60.p1.a1', '60.s1.a1', '60.s1.b1'], 'contains': ['240.a1.a1', '240.h1.a1', '240.h1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5587, -1, 7478, -1, 5364, -1, 7027, -1], 'generators': [4, 480], 'label': '960.10116.120.h1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319744
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '40.h1.a1', '60.h1.a1', '60.h1.b1', '60.k1.a1', '60.n1.a1', '60.t1.a1', '60.t1.b1', '60.v1.a1'], 'contains': ['240.a1.a1', '240.k1.a1', '240.k1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6133, -1, 4932, -1, 6213, -1, 6552, -1], 'generators': [404, 480], 'label': '960.10116.120.i1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.i1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319745
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '40.i1.a1', '60.f1.b1', '60.h1.a1', '60.o1.a1', '60.q1.a1', '60.s1.a1', '60.u1.b1', '60.w1.a1'], 'contains': ['240.a1.a1', '240.l1.a1', '240.l1.c1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6442, -1, 4882, -1, 5849, -1, 6125, -1], 'generators': [406, 480], 'label': '960.10116.120.j1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.j1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319746
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '40.i1.b1', '60.f1.a1', '60.h1.b1', '60.o1.b1', '60.q1.a1', '60.s1.b1', '60.u1.a1', '60.w1.b1'], 'contains': ['240.a1.a1', '240.l1.b1', '240.l1.d1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6442, -1, 4832, -1, 5849, -1, 6356, -1], 'generators': [405, 480], 'label': '960.10116.120.j1.b1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.j1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319747
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.a1', '240.h1.b1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.a1', '8.l1.e1', '8.m1.a1', '8.m1.e1', '8.n1.a1', '8.o1.a1', '8.p1.a1', '12.x1.a1', '20.x1.a1'], 'core': '4.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 502, 1187, 9542, 1727, 1077, 8229], 'generators': [1, 640, 404, 192, 2, 488], 'label': '960.10116.4.x1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.a1', '8.l1.e1', '8.m1.a1', '8.m1.e1', '8.n1.a1', '8.o1.a1', '8.p1.a1', '20.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.a1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319748
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '40.j1.a1', '60.g1.a1', '60.i1.b1', '60.l1.b1', '60.o1.a1', '60.r1.a1', '60.t1.a1', '60.w1.b1'], 'contains': ['240.a1.a1', '240.i1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5128, -1, 7071, -1, 5468, -1, 7217, -1], 'generators': [6, 480], 'label': '960.10116.120.k1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.k1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319749
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '40.j1.b1', '60.g1.b1', '60.i1.a1', '60.l1.a1', '60.o1.b1', '60.r1.a1', '60.t1.b1', '60.w1.a1'], 'contains': ['240.a1.a1', '240.i1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5128, -1, 5566, -1, 5468, -1, 7269, -1], 'generators': [5, 480], 'label': '960.10116.120.k1.b1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.k1.b1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319750
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '40.k1.a1', '60.i1.a1', '60.i1.b1', '60.j1.a1', '60.p1.a1', '60.u1.a1', '60.u1.b1', '60.v1.a1'], 'contains': ['240.a1.a1', '240.p1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1998, -1, 8378, -1, 4498, -1, 8170, -1], 'generators': [7, 488], 'label': '960.10116.120.l1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '40.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.l1.a1', 'projective_image': '240.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319751
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '40.q1.a1', '60.g1.a1'], 'contains': ['240.e1.a1', '240.h1.a1', '240.i1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5307, -1, 6365, -1, 3312, -1, 5249, -1], 'generators': [2, 4], 'label': '960.10116.120.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '120.m1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319752
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '40.q1.b1', '60.g1.a1'], 'contains': ['240.e1.a1', '240.h1.b1', '240.i1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5307, -1, 6305, -1, 3312, -1, 5337, -1], 'generators': [2, 484], 'label': '960.10116.120.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '120.m1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319753
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.c1', '40.q1.c1', '60.g1.b1'], 'contains': ['240.e1.b1', '240.h1.a1', '240.i1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5307, -1, 4429, -1, 3312, -1, 4957, -1], 'generators': [1, 4], 'label': '960.10116.120.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '120.m1.c1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319754
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.d1', '40.q1.d1', '60.g1.b1'], 'contains': ['240.e1.b1', '240.h1.b1', '240.i1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5307, -1, 4500, -1, 3312, -1, 5097, -1], 'generators': [1, 484], 'label': '960.10116.120.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '120.m1.d1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.m1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319755
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '40.r1.a1', '60.m1.a1'], 'contains': ['240.f1.a1', '240.g1.a1', '240.h1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2267, -1, 7178, -1, 3075, -1, 5389, -1], 'generators': [731, 4], 'label': '960.10116.120.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '120.n1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319756
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '40.r1.b1', '60.m1.a1'], 'contains': ['240.f1.a1', '240.g1.a1', '240.h1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2267, -1, 7225, -1, 3075, -1, 5475, -1], 'generators': [731, 484], 'label': '960.10116.120.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '120.n1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319757
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '40.l1.a1', '60.f1.a1', '60.x1.a1', '60.x1.c1'], 'contains': ['240.b1.a1', '240.j1.a1', '240.l1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 1777, -1, 7074, -1, 2980, -1], 'generators': [405, 2], 'label': '960.10116.120.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319758
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.b1', '240.h1.a1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.b1', '8.l1.f1', '8.m1.b1', '8.m1.f1', '8.n1.a1', '8.o1.c1', '8.p1.b1', '12.x1.b1', '20.x1.b1'], 'core': '4.x1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 1307, 2503, 9542, 1727, 714, 7595], 'generators': [1, 640, 884, 192, 2, 488], 'label': '960.10116.4.x1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.b1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.b1', '8.l1.f1', '8.m1.b1', '8.m1.f1', '8.n1.a1', '8.o1.c1', '8.p1.b1', '20.x1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.b1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319759
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.b1', '40.l1.b1', '60.f1.a1', '60.x1.b1', '60.x1.d1'], 'contains': ['240.b1.a1', '240.j1.b1', '240.l1.d1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 3257, -1, 7074, -1, 3259, -1], 'generators': [885, 2], 'label': '960.10116.120.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319760
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.c1', '40.l1.c1', '60.f1.a1', '60.x1.e1', '60.x1.g1'], 'contains': ['240.b1.b1', '240.j1.a1', '240.l1.d1'], 'core': '240.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 3610, -1, 7074, -1, 3933, -1], 'generators': [885, 482], 'label': '960.10116.120.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319761
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.d1', '40.l1.d1', '60.f1.a1', '60.x1.f1', '60.x1.h1'], 'contains': ['240.b1.b1', '240.j1.b1', '240.l1.b1'], 'core': '240.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 1825, -1, 7074, -1, 2791, -1], 'generators': [405, 482], 'label': '960.10116.120.o1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319762
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.e1', '40.l1.e1', '60.f1.b1', '60.x1.a1', '60.x1.e1'], 'contains': ['240.b1.c1', '240.j1.a1', '240.l1.a1'], 'core': '240.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 2084, -1, 7074, -1, 3140, -1], 'generators': [1, 406], 'label': '960.10116.120.o1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.e1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319763
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.f1', '40.l1.f1', '60.f1.b1', '60.x1.b1', '60.x1.f1'], 'contains': ['240.b1.c1', '240.j1.b1', '240.l1.c1'], 'core': '240.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 2544, -1, 7074, -1, 2819, -1], 'generators': [1, 886], 'label': '960.10116.120.o1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.f1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319764
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.g1', '40.l1.g1', '60.f1.b1', '60.x1.c1', '60.x1.g1'], 'contains': ['240.b1.d1', '240.j1.a1', '240.l1.c1'], 'core': '240.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 3504, -1, 7074, -1, 3790, -1], 'generators': [481, 886], 'label': '960.10116.120.o1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.g1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319765
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.h1', '40.l1.h1', '60.f1.b1', '60.x1.d1', '60.x1.h1'], 'contains': ['240.b1.d1', '240.j1.b1', '240.l1.a1'], 'core': '240.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 2506, -1, 7074, -1, 3060, -1], 'generators': [481, 406], 'label': '960.10116.120.o1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.l1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.o1.h1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.o1.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319766
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '40.m1.a1', '60.h1.a1', '60.x1.a1', '60.x1.d1'], 'contains': ['240.b1.a1', '240.k1.a1', '240.l1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 1911, -1, 7428, -1, 3628, -1], 'generators': [2, 404], 'label': '960.10116.120.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319784
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '40.s1.a1', '60.a1.a1'], 'contains': ['240.d1.a1', '240.m1.a1', '240.o1.a1'], 'core': '240.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1208, -1, 8965, -1, 1719, -1, 9117, -1], 'generators': [2, 240], 'label': '960.10116.120.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '120.s1.a1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319767
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.b1', '40.m1.b1', '60.h1.a1', '60.x1.b1', '60.x1.c1'], 'contains': ['240.b1.a1', '240.k1.b1', '240.l1.c1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 2690, -1, 7428, -1, 2751, -1], 'generators': [2, 884], 'label': '960.10116.120.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319768
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.c1', '40.m1.c1', '60.h1.a1', '60.x1.f1', '60.x1.g1'], 'contains': ['240.b1.b1', '240.k1.a1', '240.l1.c1'], 'core': '240.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 2875, -1, 7428, -1, 3893, -1], 'generators': [482, 404], 'label': '960.10116.120.p1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319769
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.b1', '240.h1.a1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.a1', '8.l1.g1', '8.m1.b1', '8.m1.h1', '8.n1.b1', '8.o1.b1', '8.p1.d1', '12.x1.c1', '20.x1.c1'], 'core': '4.x1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 926, 372, 9542, 1727, 1367, 8449], 'generators': [481, 640, 884, 192, 2, 488], 'label': '960.10116.4.x1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.c1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.g1', '8.l1.a1', '8.m1.h1', '8.m1.b1', '8.n1.b1', '8.o1.b1', '8.p1.d1', '20.x1.c1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.c1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319770
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.d1', '40.m1.d1', '60.h1.a1', '60.x1.e1', '60.x1.h1'], 'contains': ['240.b1.b1', '240.k1.b1', '240.l1.a1'], 'core': '240.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 2580, -1, 7428, -1, 2859, -1], 'generators': [482, 884], 'label': '960.10116.120.p1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319771
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.e1', '40.m1.e1', '60.h1.b1', '60.x1.a1', '60.x1.f1'], 'contains': ['240.b1.c1', '240.k1.a1', '240.l1.b1'], 'core': '240.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 1470, -1, 7428, -1, 3020, -1], 'generators': [1, 404], 'label': '960.10116.120.p1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.e1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319772
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.f1', '40.m1.f1', '60.h1.b1', '60.x1.b1', '60.x1.e1'], 'contains': ['240.b1.c1', '240.k1.b1', '240.l1.d1'], 'core': '240.b1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 3377, -1, 7428, -1, 2912, -1], 'generators': [1, 884], 'label': '960.10116.120.p1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.f1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319773
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.g1', '40.m1.g1', '60.h1.b1', '60.x1.d1', '60.x1.g1'], 'contains': ['240.b1.d1', '240.k1.a1', '240.l1.d1'], 'core': '240.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 3548, -1, 7428, -1, 4053, -1], 'generators': [481, 404], 'label': '960.10116.120.p1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.g1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319774
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.h1', '40.m1.h1', '60.h1.b1', '60.x1.c1', '60.x1.h1'], 'contains': ['240.b1.d1', '240.k1.b1', '240.l1.b1'], 'core': '240.b1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [8195, -1, 2023, -1, 7428, -1, 2539, -1], 'generators': [481, 884], 'label': '960.10116.120.p1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.m1.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.p1.h1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.p1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319775
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '40.o1.a1', '60.k1.a1', '60.x1.a1', '60.x1.g1'], 'contains': ['240.c1.a1', '240.j1.a1', '240.k1.a1'], 'core': '240.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9522, -1, 2740, -1, 8455, -1, 3520, -1], 'generators': [3, 404], 'label': '960.10116.120.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.q1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319776
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.b1', '40.o1.b1', '60.k1.a1', '60.x1.c1', '60.x1.e1'], 'contains': ['240.c1.b1', '240.j1.a1', '240.k1.b1'], 'core': '240.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9522, -1, 3293, -1, 8455, -1, 3415, -1], 'generators': [483, 884], 'label': '960.10116.120.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.q1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319777
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.c1', '40.o1.c1', '60.k1.a1', '60.x1.b1', '60.x1.h1'], 'contains': ['240.c1.a1', '240.j1.b1', '240.k1.b1'], 'core': '240.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9522, -1, 2259, -1, 8455, -1, 2486, -1], 'generators': [3, 884], 'label': '960.10116.120.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.o1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.q1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319778
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.d1', '40.o1.d1', '60.k1.a1', '60.x1.d1', '60.x1.f1'], 'contains': ['240.c1.b1', '240.j1.b1', '240.k1.a1'], 'core': '240.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9522, -1, 2627, -1, 8455, -1, 4001, -1], 'generators': [483, 404], 'label': '960.10116.120.q1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.o1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.q1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.q1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319779
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '40.p1.a1', '60.q1.a1', '60.x1.a1', '60.x1.h1'], 'contains': ['240.c1.a1', '240.l1.a1', '240.l1.b1'], 'core': '240.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9665, -1, 1098, -1, 8720, -1, 2579, -1], 'generators': [405, 406], 'label': '960.10116.120.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.r1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319780
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.a1', '240.h1.b1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.b1', '8.l1.h1', '8.m1.a1', '8.m1.g1', '8.n1.b1', '8.o1.d1', '8.p1.c1', '12.x1.d1', '20.x1.d1'], 'core': '4.x1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 1653, 1546, 9542, 1727, 1783, 8120], 'generators': [481, 640, 404, 192, 2, 488], 'label': '960.10116.4.x1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.d1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.h1', '8.l1.b1', '8.m1.g1', '8.m1.a1', '8.n1.b1', '8.o1.d1', '8.p1.c1', '20.x1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.d1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319781
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.b1', '40.p1.b1', '60.q1.a1', '60.x1.b1', '60.x1.g1'], 'contains': ['240.c1.a1', '240.l1.c1', '240.l1.d1'], 'core': '240.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9665, -1, 3464, -1, 8720, -1, 3231, -1], 'generators': [885, 886], 'label': '960.10116.120.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.r1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319782
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.c1', '40.p1.c1', '60.q1.a1', '60.x1.d1', '60.x1.e1'], 'contains': ['240.c1.b1', '240.l1.a1', '240.l1.d1'], 'core': '240.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9665, -1, 3431, -1, 8720, -1, 3961, -1], 'generators': [885, 406], 'label': '960.10116.120.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.p1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.r1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319783
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '120.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1536, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.d1', '40.p1.d1', '60.q1.a1', '60.x1.c1', '60.x1.f1'], 'contains': ['240.c1.b1', '240.l1.b1', '240.l1.c1'], 'core': '240.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9665, -1, 2059, -1, 8720, -1, 3375, -1], 'generators': [405, 886], 'label': '960.10116.120.r1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.p1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '120.r1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.r1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319785
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '40.s1.b1', '60.a1.a1'], 'contains': ['240.d1.b1', '240.m1.a1', '240.o1.a1'], 'core': '240.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1208, -1, 9065, -1, 1719, -1, 9031, -1], 'generators': [2, 728], 'label': '960.10116.120.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '120.s1.b1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319786
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.c1', '40.s1.c1', '60.a1.b1'], 'contains': ['240.d1.a1', '240.m1.b1', '240.o1.b1'], 'core': '240.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1208, -1, 9363, -1, 1719, -1, 9480, -1], 'generators': [1, 240], 'label': '960.10116.120.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '120.s1.c1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319787
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '120.s1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.d1', '40.s1.d1', '60.a1.b1'], 'contains': ['240.d1.b1', '240.m1.b1', '240.o1.b1'], 'core': '240.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1208, -1, 9422, -1, 1719, -1, 9427, -1], 'generators': [1, 728], 'label': '960.10116.120.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '120.s1.d1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.s1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319788
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '40.t1.a1', '60.j1.a1'], 'contains': ['240.d1.a1', '240.n1.a1', '240.p1.a1'], 'core': '240.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [609, -1, 9151, -1, 1100, -1, 8829, -1], 'generators': [7, 240], 'label': '960.10116.120.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '120.t1.a1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319789
    {'ambient': '960.10116', 'aut_centralizer_order': 256, 'aut_label': '120.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 3072, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.b1', '40.t1.b1', '60.j1.a1'], 'contains': ['240.d1.b1', '240.n1.a1', '240.p1.a1'], 'core': '240.d1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [609, -1, 9288, -1, 1100, -1, 8742, -1], 'generators': [7, 728], 'label': '960.10116.120.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '120.t1.b1', 'projective_image': '240.170', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.t1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319790
    {'ambient': '960.10116', 'aut_centralizer_order': 6144, 'aut_label': '160.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '80.a1.a1', '80.b1.a1', '80.b1.b1', '80.i1.a1', '80.i1.b1', '80.j1.a1', '80.k1.a1', '80.l1.a1', '80.l1.b1'], 'contains': ['320.a1.a1', '480.a1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3220, 3294, 6182, 4572, 2524, 4509, 5116, 3608], 'generators': [8, 640], 'label': '960.10116.160.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': ['32.a1.a1', '80.a1.a1', '80.b1.a1', '80.b1.b1'], 'normal_contains': ['320.a1.a1', '480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '480.1160', 'quotient_action_image': '2.1', 'quotient_action_kernel': '80.48', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319791
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.b1', '240.h1.a1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.c1', '8.l1.e1', '8.m1.d1', '8.m1.f1', '8.n1.c1', '8.o1.b1', '8.p1.c1', '12.x1.e1', '20.x1.e1'], 'core': '4.x1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 1890, 1796, 9542, 1727, 1567, 7705], 'generators': [1, 640, 884, 192, 482, 488], 'label': '960.10116.4.x1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.e1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.c1', '8.l1.e1', '8.m1.d1', '8.m1.f1', '8.n1.c1', '8.o1.b1', '8.p1.c1', '20.x1.e1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.e1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319792
    {'ambient': '960.10116', 'aut_centralizer_order': 6144, 'aut_label': '160.b1', 'aut_quo_index': 672, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '80.a1.a1', '80.c1.a1', '80.c1.b1', '80.c1.c1', '80.c1.d1', '80.d1.a1', '80.d1.b1', '80.e1.a1', '80.e1.b1', '80.f1.a1', '80.f1.b1', '80.g1.a1', '80.g1.b1', '80.g1.c1', '80.g1.d1'], 'contains': ['320.a1.a1', '480.b1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7695, 6777, 2355, 2517, 6859, 3048, 3336, 5955], 'generators': [488, 640], 'label': '960.10116.160.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.b1.a1', 'normal_contained_in': ['32.b1.a1', '80.a1.a1', '80.c1.d1', '80.c1.a1', '80.c1.b1', '80.c1.c1', '80.d1.a1', '80.d1.b1', '80.e1.b1', '80.e1.a1', '80.f1.b1', '80.f1.a1', '80.g1.a1', '80.g1.c1', '80.g1.b1', '80.g1.d1'], 'normal_contains': ['320.a1.a1', '480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.b1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '80.45', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319793
    {'ambient': '960.10116', 'aut_centralizer_order': 6144, 'aut_label': '160.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '80.a1.a1', '80.h1.a1', '80.h1.b1', '80.m1.a1', '80.m1.b1', '80.n1.a1', '80.o1.a1', '80.o1.b1', '80.p1.a1'], 'contains': ['320.a1.a1', '480.c1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [989, 3147, 9716, 8268, 1425, 3138, 9216, 3087], 'generators': [480, 640], 'label': '960.10116.160.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.c1.a1', 'normal_contained_in': ['32.c1.a1', '80.a1.a1', '80.h1.b1', '80.h1.a1'], 'normal_contains': ['320.a1.a1', '480.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.c1.a1', 'projective_image': '480.1155', 'quotient_action_image': '2.1', 'quotient_action_kernel': '80.46', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319794
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '80.c1.a1', '80.i1.a1', '80.m1.a1'], 'contains': ['320.a1.a1', '480.d1.a1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2759, -1, 5476, -1, 2445, -1, 4706, -1], 'generators': [2, 640], 'label': '960.10116.160.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '160.d1.a1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319795
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '80.c1.b1', '80.i1.a1', '80.m1.a1'], 'contains': ['320.a1.a1', '480.d1.b1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2759, -1, 5259, -1, 2445, -1, 4762, -1], 'generators': [482, 640], 'label': '960.10116.160.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '160.d1.b1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319796
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '80.c1.c1', '80.i1.b1', '80.m1.b1'], 'contains': ['320.a1.a1', '480.d1.c1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2759, -1, 4290, -1, 2445, -1, 4678, -1], 'generators': [1, 640], 'label': '960.10116.160.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '160.d1.c1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319797
    {'ambient': '960.10116', 'aut_centralizer_order': 768, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '4.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '80.c1.d1', '80.i1.b1', '80.m1.b1'], 'contains': ['320.a1.a1', '480.d1.d1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2759, -1, 4241, -1, 2445, -1, 4734, -1], 'generators': [481, 640], 'label': '960.10116.160.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '160.d1.d1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319798
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2048, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '80.d1.a1', '80.j1.a1', '80.n1.a1'], 'contains': ['320.a1.a1', '480.e1.a1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [931, -1, 6496, -1, 2197, -1, 4883, -1], 'generators': [407, 640], 'label': '960.10116.160.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '160.e1.a1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319799
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2048, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '80.d1.b1', '80.j1.a1', '80.n1.a1'], 'contains': ['320.a1.a1', '480.e1.b1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [931, -1, 6805, -1, 2197, -1, 4855, -1], 'generators': [887, 640], 'label': '960.10116.160.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '160.e1.b1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319800
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.d1.b1', '96.d1.c1', '96.d1.d1', '96.e1.a1', '96.e1.b1'], 'contains': ['960.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2415, 5171, 5382, 4922, 2531, 2883, 4580, 3603], 'generators': [192], 'label': '960.10116.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.c1.a1', '96.a1.a1', '96.b1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.1095', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.1095', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319801
    {'ambient': '960.10116', 'aut_centralizer_order': 12288, 'aut_label': '240.a1', 'aut_quo_index': 672, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.a1.b1', '120.b1.a1', '120.c1.a1', '120.d1.a1', '120.d1.b1', '120.e1.a1', '120.g1.a1', '120.h1.a1', '120.i1.a1', '120.j1.a1', '120.j1.b1', '120.k1.a1', '120.k1.b1', '120.l1.a1'], 'contains': ['480.a1.a1', '480.b1.a1', '480.c1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4146, 6542, 5219, 8532, 5147, 1882, 6584, 3037], 'generators': [488, 480], 'label': '960.10116.240.a1.a1', 'mobius_quo': 2, 'mobius_sub': 192, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.b1', '120.a1.a1', '120.b1.a1', '120.d1.a1', '120.d1.b1', '120.e1.a1', '120.c1.a1'], 'normal_contains': ['480.c1.a1', '480.a1.a1', '480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '240.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.206', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319802
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.a1', '240.h1.b1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.d1', '8.l1.f1', '8.m1.c1', '8.m1.e1', '8.n1.c1', '8.o1.d1', '8.p1.d1', '12.x1.f1', '20.x1.f1'], 'core': '4.x1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 842, 3371, 9542, 1727, 1476, 8339], 'generators': [1, 640, 404, 192, 482, 488], 'label': '960.10116.4.x1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.f1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.d1', '8.l1.f1', '8.m1.c1', '8.m1.e1', '8.n1.c1', '8.o1.d1', '8.p1.d1', '20.x1.f1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.f1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319803
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.c1.a1', '120.a1.a1', '120.f1.a1', '120.f1.b1', '120.o1.a1', '120.o1.b1', '120.p1.a1', '120.p1.b1'], 'contains': ['480.b1.a1', '480.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7750, 7567, 2216, 3956, 6985, 1412, 3299, 5058], 'generators': [2, 488], 'label': '960.10116.240.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.b1.a1', 'normal_contained_in': ['48.b1.a1', '80.c1.a1', '120.a1.a1', '120.f1.b1', '120.f1.a1'], 'normal_contains': ['480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.22', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319804
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.b1', '80.c1.b1', '120.a1.a1', '120.f1.c1', '120.f1.d1', '120.o1.c1', '120.o1.d1', '120.p1.c1', '120.p1.d1'], 'contains': ['480.b1.a1', '480.d1.b1'], 'core': '240.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7750, 7567, 2999, 4337, 6985, 1412, 3467, 4750], 'generators': [482, 488], 'label': '960.10116.240.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.b1.b1', 'normal_contained_in': ['48.b1.b1', '80.c1.b1', '120.a1.a1', '120.f1.d1', '120.f1.c1'], 'normal_contains': ['480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.22', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319805
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.c1', '80.c1.c1', '120.a1.b1', '120.f1.a1', '120.f1.c1', '120.o1.e1', '120.o1.f1', '120.p1.e1', '120.p1.f1'], 'contains': ['480.b1.a1', '480.d1.c1'], 'core': '240.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7750, 7567, 2123, 4678, 6985, 1412, 3100, 4816], 'generators': [1, 488], 'label': '960.10116.240.b1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.b1.c1', 'normal_contained_in': ['48.b1.c1', '80.c1.c1', '120.a1.b1', '120.f1.a1', '120.f1.c1'], 'normal_contains': ['480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.c1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.22', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319806
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.b1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.d1', '80.c1.d1', '120.a1.b1', '120.f1.b1', '120.f1.d1', '120.o1.g1', '120.o1.h1', '120.p1.g1', '120.p1.h1'], 'contains': ['480.b1.a1', '480.d1.d1'], 'core': '240.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7750, 7567, 3237, 3802, 6985, 1412, 3680, 4959], 'generators': [481, 488], 'label': '960.10116.240.b1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.b1.d1', 'normal_contained_in': ['48.b1.d1', '80.c1.d1', '120.a1.b1', '120.f1.b1', '120.f1.d1'], 'normal_contains': ['480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.d1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.22', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319807
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '240.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '80.e1.a1', '120.c1.a1', '120.f1.a1', '120.f1.d1', '120.q1.a1', '120.q1.c1', '120.r1.a1', '120.r1.b1'], 'contains': ['480.b1.a1'], 'core': '240.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9454, 8817, 2268, 4220, 8541, 1276, 2977, 4631], 'generators': [3], 'label': '960.10116.240.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.c1.a1', 'normal_contained_in': ['48.c1.a1', '80.e1.a1', '120.c1.a1', '120.f1.d1', '120.f1.a1'], 'normal_contains': ['480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.c1.a1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.22', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319808
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '240.c1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '80.e1.b1', '120.c1.a1', '120.f1.b1', '120.f1.c1', '120.q1.b1', '120.q1.d1', '120.r1.c1', '120.r1.d1'], 'contains': ['480.b1.a1'], 'core': '240.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9454, 8817, 3079, 4065, 8541, 1276, 3751, 5148], 'generators': [483], 'label': '960.10116.240.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.c1.b1', 'normal_contained_in': ['48.c1.b1', '80.e1.b1', '120.c1.a1', '120.f1.b1', '120.f1.c1'], 'normal_contains': ['480.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.c1.b1', 'projective_image': '480.1151', 'quotient_action_image': '2.1', 'quotient_action_kernel': '120.22', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319809
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '240.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '1.a1.a1', 'complements': ['4.x1.a1', '4.x1.d1', '4.x1.f1', '4.x1.g1', '4.x1.b1', '4.x1.c1', '4.x1.e1', '4.x1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '80.h1.a1', '120.b1.a1', '120.s1.a1', '120.s1.c1', '120.t1.a1'], 'contains': ['480.c1.a1'], 'core': '240.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [889, 4426, 9121, 8845, 1480, 2645, 9117, 1729], 'generators': [240], 'label': '960.10116.240.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.d1.a1', 'normal_contained_in': ['48.d1.a1', '80.h1.a1', '120.b1.a1'], 'normal_contains': ['480.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.d1.a1', 'projective_image': '240.170', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.170', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319810
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '240.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '1.a1.a1', 'complements': ['4.x1.b1', '4.x1.c1', '4.x1.e1', '4.x1.h1', '4.x1.a1', '4.x1.d1', '4.x1.f1', '4.x1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '80.h1.b1', '120.b1.a1', '120.s1.b1', '120.s1.d1', '120.t1.b1'], 'contains': ['480.c1.a1'], 'core': '240.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [889, 4426, 9305, 8754, 1480, 2645, 8931, 1668], 'generators': [728], 'label': '960.10116.240.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '240.d1.b1', 'normal_contained_in': ['48.d1.b1', '80.h1.b1', '120.b1.a1'], 'normal_contains': ['480.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.d1.b1', 'projective_image': '240.170', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.170', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319811
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '80.i1.a1', '120.a1.a1', '120.m1.a1', '120.m1.b1'], 'contains': ['480.a1.a1', '480.d1.a1', '480.d1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3403, -1, 5979, -1, 2960, -1, 5145, -1], 'generators': [2, 8], 'label': '960.10116.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '240.e1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319812
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '80.i1.b1', '120.a1.b1', '120.m1.c1', '120.m1.d1'], 'contains': ['480.a1.a1', '480.d1.c1', '480.d1.d1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3403, -1, 4448, -1, 2960, -1, 4825, -1], 'generators': [1, 8], 'label': '960.10116.240.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '240.e1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319845
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '160.e1.a1', '240.f1.a1', '240.j1.a1', '240.n1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [961, -1, 6549, -1, 2476, -1, 4864, -1], 'generators': [407], 'label': '960.10116.480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '480.e1.a1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319813
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.a1', '240.h1.b1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.c1', '8.l1.g1', '8.m1.c1', '8.m1.g1', '8.n1.d1', '8.o1.a1', '8.p1.b1', '12.x1.g1', '20.x1.g1'], 'core': '4.x1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 2511, 1036, 9542, 1727, 1684, 7189], 'generators': [481, 640, 404, 192, 482, 488], 'label': '960.10116.4.x1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.g1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.g1', '8.l1.c1', '8.m1.g1', '8.m1.c1', '8.n1.d1', '8.o1.a1', '8.p1.b1', '20.x1.g1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.g1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319814
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '80.j1.a1', '120.g1.a1', '120.n1.a1', '120.n1.b1'], 'contains': ['480.a1.a1', '480.e1.a1', '480.e1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2064, -1, 6734, -1, 2698, -1, 5260, -1], 'generators': [407, 8], 'label': '960.10116.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '240.f1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319815
    {'ambient': '960.10116', 'aut_centralizer_order': 3072, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '80.k1.a1', '120.e1.a1', '120.n1.a1', '120.n1.b1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2267, -1, 7183, -1, 2902, -1, 5410, -1], 'generators': [731], 'label': '960.10116.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '240.g1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319816
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '80.b1.a1', '120.h1.a1', '120.m1.a1', '120.m1.c1', '120.n1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4876, -1, 6411, -1, 3117, -1, 5175, -1], 'generators': [4], 'label': '960.10116.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.h1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319817
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.b1', '80.b1.b1', '120.h1.a1', '120.m1.b1', '120.m1.d1', '120.n1.b1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4876, -1, 6693, -1, 3117, -1, 5230, -1], 'generators': [484], 'label': '960.10116.240.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.h1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319818
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '80.l1.a1', '120.k1.a1', '120.m1.a1', '120.m1.b1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4695, -1, 6305, -1, 3227, -1, 5203, -1], 'generators': [6], 'label': '960.10116.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '240.i1.a1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319819
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '80.l1.b1', '120.k1.b1', '120.m1.c1', '120.m1.d1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4695, -1, 4415, -1, 3227, -1, 5044, -1], 'generators': [5], 'label': '960.10116.240.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '240.i1.b1', 'projective_image': '480.1160', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319820
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '80.d1.a1', '120.g1.a1', '120.o1.a1', '120.o1.c1', '120.o1.e1', '120.o1.g1', '120.q1.a1', '120.q1.b1'], 'contains': ['480.b1.a1', '480.e1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6373, -1, 2847, -1, 6689, -1, 3520, -1], 'generators': [407, 488], 'label': '960.10116.240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.j1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319821
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.b1', '80.d1.b1', '120.g1.a1', '120.o1.b1', '120.o1.d1', '120.o1.f1', '120.o1.h1', '120.q1.c1', '120.q1.d1'], 'contains': ['480.b1.a1', '480.e1.b1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6373, -1, 2465, -1, 6689, -1, 3060, -1], 'generators': [887, 488], 'label': '960.10116.240.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.j1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319822
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '80.f1.a1', '120.i1.a1', '120.p1.a1', '120.p1.c1', '120.p1.e1', '120.p1.g1', '120.q1.a1', '120.q1.d1'], 'contains': ['480.b1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7922, -1, 2578, -1, 7275, -1, 3817, -1], 'generators': [404], 'label': '960.10116.240.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.k1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319823
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '80.f1.b1', '120.i1.a1', '120.p1.b1', '120.p1.d1', '120.p1.f1', '120.p1.h1', '120.q1.b1', '120.q1.c1'], 'contains': ['480.b1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7922, -1, 2617, -1, 7275, -1, 2784, -1], 'generators': [884], 'label': '960.10116.240.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.k1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319824
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': ['480.d1.c1', '480.d1.d1', '480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.e1.a1', '4.m1.a1', '4.n1.a1', '4.s1.a1', '4.t1.a1', '6.d1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5761, 1850, 7390, 5893, 3591, 6994, 5604, 4355], 'generators': [2, 480, 240, 192, 4, 640, 8], 'label': '960.10116.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.d1.a1', '4.m1.a1', '4.n1.a1', '4.t1.a1', '4.s1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '24.14', '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': '12.4'}
  • id: 112319825
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '4.x1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '384.18344', 'aut_weyl_index': 32, 'centralizer': '24.b1.a1', 'complements': ['240.d1.a1', '240.d1.b1', '240.h1.b1', '240.h1.a1', '240.o1.a1', '240.i1.a1', '240.o1.b1', '240.i1.b1', '240.g1.a1', '240.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.l1.d1', '8.l1.h1', '8.m1.d1', '8.m1.h1', '8.n1.d1', '8.o1.c1', '8.p1.a1', '12.x1.h1', '20.x1.h1'], 'core': '4.x1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [9518, 8024, 780, 1309, 9542, 1727, 645, 9265], 'generators': [481, 640, 884, 192, 482, 488], 'label': '960.10116.4.x1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.x1.h1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['8.l1.h1', '8.l1.d1', '8.m1.h1', '8.m1.d1', '8.n1.d1', '8.o1.c1', '8.p1.a1', '20.x1.h1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.h1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.x1.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319826
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '80.g1.a1', '120.j1.a1', '120.o1.e1', '120.o1.h1', '120.p1.a1', '120.p1.d1', '120.r1.a1', '120.r1.c1'], 'contains': ['480.b1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7308, -1, 1999, -1, 7137, -1, 3156, -1], 'generators': [406], 'label': '960.10116.240.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.l1.a1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319827
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.b1', '80.g1.b1', '120.j1.b1', '120.o1.a1', '120.o1.d1', '120.p1.e1', '120.p1.h1', '120.r1.a1', '120.r1.d1'], 'contains': ['480.b1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7308, -1, 1804, -1, 7137, -1, 2844, -1], 'generators': [405], 'label': '960.10116.240.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.l1.b1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319828
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.c1', '80.g1.c1', '120.j1.a1', '120.o1.f1', '120.o1.g1', '120.p1.b1', '120.p1.c1', '120.r1.b1', '120.r1.d1'], 'contains': ['480.b1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7308, -1, 2725, -1, 7137, -1, 3364, -1], 'generators': [886], 'label': '960.10116.240.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.g1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.l1.c1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319829
    {'ambient': '960.10116', 'aut_centralizer_order': 512, 'aut_label': '240.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.d1', '80.g1.d1', '120.j1.b1', '120.o1.b1', '120.o1.c1', '120.p1.f1', '120.p1.g1', '120.r1.b1', '120.r1.c1'], 'contains': ['480.b1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7308, -1, 3532, -1, 7137, -1, 3717, -1], 'generators': [885], 'label': '960.10116.240.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.g1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '240.l1.d1', 'projective_image': '480.1151', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.l1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319830
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '80.m1.a1', '120.a1.a1', '120.s1.a1', '120.s1.b1'], 'contains': ['480.c1.a1', '480.d1.a1', '480.d1.b1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1351, -1, 8826, -1, 1880, -1, 8745, -1], 'generators': [2, 480], 'label': '960.10116.240.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '240.m1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319831
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.b1', '80.m1.b1', '120.a1.b1', '120.s1.c1', '120.s1.d1'], 'contains': ['480.c1.a1', '480.d1.c1', '480.d1.d1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1351, -1, 9332, -1, 1880, -1, 8960, -1], 'generators': [1, 480], 'label': '960.10116.240.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '240.m1.b1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319832
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '80.n1.a1', '120.g1.a1', '120.t1.a1', '120.t1.b1'], 'contains': ['480.c1.a1', '480.e1.a1', '480.e1.b1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [564, -1, 9168, -1, 1538, -1, 8649, -1], 'generators': [407, 480], 'label': '960.10116.240.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '240.n1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319833
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '80.o1.a1', '120.d1.a1', '120.s1.a1', '120.s1.b1'], 'contains': ['480.c1.a1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1246, -1, 9019, -1, 1664, -1, 8903, -1], 'generators': [242], 'label': '960.10116.240.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '240.o1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319834
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '240.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '80.o1.b1', '120.d1.b1', '120.s1.c1', '120.s1.d1'], 'contains': ['480.c1.a1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1246, -1, 9431, -1, 1664, -1, 9406, -1], 'generators': [241], 'label': '960.10116.240.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '240.o1.b1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.o1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319835
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '240.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '80.p1.a1', '120.l1.a1', '120.t1.a1', '120.t1.b1'], 'contains': ['480.c1.a1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [690, -1, 9249, -1, 1186, -1, 8807, -1], 'generators': [7], 'label': '960.10116.240.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '240.p1.a1', 'projective_image': '480.1155', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319836
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3072.bhn', 'aut_weyl_index': 4, 'centralizer': '24.b1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.a1.b1', '10.b1.a1', '10.b1.b1', '10.c1.a1', '10.c1.b1', '10.d1.a1', '10.d1.b1', '10.e1.a1', '10.f1.a1', '10.g1.a1', '10.h1.a1', '10.i1.a1', '10.j1.a1', '10.k1.a1', '15.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7086, 1181, 7149, 5785, 6077, 6382, 7891, 3712], 'generators': [1, 480, 488, 2, 640, 4, 240], 'label': '960.10116.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.b1', '10.a1.a1', '10.b1.b1', '10.b1.a1', '10.c1.b1', '10.c1.a1', '10.d1.b1', '10.d1.a1', '10.e1.a1', '10.f1.a1', '10.g1.a1', '10.h1.a1', '10.i1.a1', '10.j1.a1', '10.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '120.45', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319837
    {'ambient': '960.10116', 'aut_centralizer_order': 6144, 'aut_label': '320.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 6144, 'centralizer': '2.f1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1', '160.d1.a1', '160.d1.b1', '160.d1.c1', '160.d1.d1', '160.e1.a1', '160.e1.b1'], 'contains': ['960.a1.a1'], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2626, 4220, 5411, 4503, 2421, 3138, 4762, 3650], 'generators': [640], 'label': '960.10116.320.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': ['64.a1.a1', '160.c1.a1', '160.a1.a1', '160.b1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '320.a1.a1', 'projective_image': '960.10116', 'quotient_action_image': '2.1', 'quotient_action_kernel': '160.179', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319838
    {'ambient': '960.10116', 'aut_centralizer_order': 12288, 'aut_label': '480.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.e1.a1', '240.e1.b1', '240.f1.a1', '240.g1.a1', '240.h1.a1', '240.h1.b1', '240.i1.a1', '240.i1.b1'], 'contains': ['960.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3220, 5441, 6176, 6224, 2902, 2994, 5160, 3555], 'generators': [8], 'label': '960.10116.480.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '480.1160', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.1160', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319839
    {'ambient': '960.10116', 'aut_centralizer_order': 12288, 'aut_label': '480.b1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '160.b1.a1', '240.a1.a1', '240.b1.a1', '240.b1.b1', '240.b1.c1', '240.b1.d1', '240.c1.a1', '240.c1.b1', '240.j1.a1', '240.j1.b1', '240.k1.a1', '240.k1.b1', '240.l1.a1', '240.l1.b1', '240.l1.c1', '240.l1.d1'], 'contains': ['960.a1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7398, 7362, 2597, 4158, 6919, 1818, 3350, 4843], 'generators': [488], 'label': '960.10116.480.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.b1.a1', 'normal_contained_in': ['96.b1.a1', '160.b1.a1', '240.a1.a1', '240.b1.d1', '240.b1.a1', '240.b1.b1', '240.b1.c1', '240.c1.b1', '240.c1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.b1.a1', 'projective_image': '480.1151', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.1151', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319840
    {'ambient': '960.10116', 'aut_centralizer_order': 12288, 'aut_label': '480.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '160.c1.a1', '240.a1.a1', '240.d1.a1', '240.d1.b1', '240.m1.a1', '240.m1.b1', '240.n1.a1', '240.o1.a1', '240.o1.b1', '240.p1.a1'], 'contains': ['960.a1.a1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1048, 4965, 9214, 8630, 1603, 2772, 8888, 3009], 'generators': [480], 'label': '960.10116.480.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.c1.a1', 'normal_contained_in': ['96.c1.a1', '160.c1.a1', '240.a1.a1', '240.d1.b1', '240.d1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.c1.a1', 'projective_image': '480.1155', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.1155', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319841
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '160.d1.a1', '240.b1.a1', '240.e1.a1', '240.m1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2714, -1, 5464, -1, 2585, -1, 4706, -1], 'generators': [2], 'label': '960.10116.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '480.d1.a1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319842
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.b1', '160.d1.b1', '240.b1.b1', '240.e1.a1', '240.m1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2714, -1, 5297, -1, 2585, -1, 4817, -1], 'generators': [482], 'label': '960.10116.480.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '480.d1.b1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319843
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.c1', '160.d1.c1', '240.b1.c1', '240.e1.b1', '240.m1.b1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2714, -1, 4362, -1, 2585, -1, 4678, -1], 'generators': [1], 'label': '960.10116.480.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '480.d1.c1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319844
    {'ambient': '960.10116', 'aut_centralizer_order': 1536, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '2.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.d1', '160.d1.d1', '240.b1.d1', '240.e1.b1', '240.m1.b1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2714, -1, 4244, -1, 2585, -1, 4734, -1], 'generators': [481], 'label': '960.10116.480.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '480.d1.d1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.d1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319846
    {'ambient': '960.10116', 'aut_centralizer_order': 1024, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 12288, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.b1', '160.e1.b1', '240.f1.a1', '240.j1.b1', '240.n1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [961, -1, 6692, -1, 2476, -1, 4790, -1], 'generators': [887], 'label': '960.10116.480.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '480.e1.b1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319847
    {'ambient': '960.10116', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 24, 'centralizer': '4.m1.a1', 'complements': ['160.e1.a1', '160.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.b1.a1', '12.b1.b1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5340, 9610, 7552, 9499, 7196, 688, 7521, 485], 'generators': [1, 480, 240, 192, 2, 488], 'label': '960.10116.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.f1.a1'], 'normal_contains': ['12.a1.b1', '12.a1.a1', '12.b1.b1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319848
    {'ambient': '960.10116', 'aut_centralizer_order': None, 'aut_label': '960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '320.a1.a1', '480.a1.a1', '480.b1.a1', '480.c1.a1', '480.d1.a1', '480.d1.b1', '480.d1.c1', '480.d1.d1', '480.e1.a1', '480.e1.b1'], 'contains': [], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2626, 5171, 5430, 4922, 2531, 2883, 4762, 3603], 'generators': [], 'label': '960.10116.960.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '960.a1.a1', 'normal_contained_in': ['192.a1.a1', '320.a1.a1', '480.c1.a1', '480.a1.a1', '480.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '960.a1.a1', 'projective_image': '960.10116', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 112319849
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.i1.a1', '12.j1.a1', '12.l1.a1', '12.o1.b1', '12.u1.a1', '30.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2252, -1, 5725, -1, 4584, -1, 7458, -1], 'generators': [5, 480, 240, 192, 2, 8], 'label': '960.10116.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319850
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.f1.b1', '12.i1.b1', '12.j1.a1', '12.l1.b1', '12.o1.a1', '12.u1.b1', '30.b1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2252, -1, 7413, -1, 4584, -1, 7395, -1], 'generators': [1, 480, 240, 192, 6, 488], 'label': '960.10116.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319851
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.f1.a1', '12.g1.a1', '12.l1.b1', '12.m1.a1', '12.s1.b1', '12.w1.b1', '30.c1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3731, -1, 5961, -1, 5066, -1, 5197, -1], 'generators': [241, 480, 4, 192, 2, 488], 'label': '960.10116.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319852
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.b1.b1', '12.f1.b1', '12.g1.b1', '12.l1.a1', '12.m1.a1', '12.s1.a1', '12.w1.a1', '30.c1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3731, -1, 5038, -1, 5066, -1, 5070, -1], 'generators': [1, 480, 4, 192, 242, 488], 'label': '960.10116.6.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319853
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '6.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.h1.a1', '12.n1.a1', '12.o1.a1', '12.s1.a1', '12.t1.a1', '30.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6146, -1, 7061, -1, 5665, -1, 5626, -1], 'generators': [2, 480, 240, 192, 4, 8], 'label': '960.10116.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '24.14', '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': '2.1'}
  • id: 112319854
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '6.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.g1.b1', '12.h1.b1', '12.n1.a1', '12.o1.b1', '12.s1.b1', '12.t1.b1', '30.d1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6146, -1, 5470, -1, 5665, -1, 6274, -1], 'generators': [1, 480, 240, 192, 4, 8], 'label': '960.10116.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '24.14', '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': '2.1'}
  • id: 112319855
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.h1.a1', '12.i1.a1', '12.t1.b1', '12.u1.b1', '12.v1.a1', '12.w1.a1', '30.e1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2688, -1, 5797, -1, 5264, -1, 6368, -1], 'generators': [241, 480, 404, 192, 2, 488], 'label': '960.10116.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319856
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '12.a1.b1', 'complements': ['480.d1.a1', '480.d1.b1', '480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.d1.b1', '4.e1.b1', '4.m1.a1', '4.n1.b1', '4.s1.b1', '4.t1.b1', '6.d1.b1', '10.c1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5761, 1850, 5650, 5310, 3591, 6994, 6250, 4178], 'generators': [1, 480, 240, 192, 4, 640, 8], 'label': '960.10116.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.e1.b1', '4.d1.b1', '4.m1.a1', '4.n1.b1', '4.t1.b1', '4.s1.b1', '10.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '24.14', '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': '12.4'}
  • id: 112319857
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.a1.a1'], 'contains': ['12.b1.b1', '12.h1.b1', '12.i1.b1', '12.t1.a1', '12.u1.a1', '12.v1.a1', '12.w1.b1', '30.e1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2688, -1, 6621, -1, 5264, -1, 5882, -1], 'generators': [1, 480, 404, 192, 242, 488], 'label': '960.10116.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319858
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 24, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.f1.b1', '12.h1.a1', '12.h1.b1', '12.k1.a1', '12.q1.a1', '12.x1.a1', '12.x1.b1', '12.x1.c1', '12.x1.d1', '12.x1.e1', '12.x1.f1', '12.x1.g1', '12.x1.h1', '30.f1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9036, -1, 3192, -1, 8629, -1, 3476, -1], 'generators': [1, 488, 404, 480, 2, 192], 'label': '960.10116.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319859
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 24, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.g1.b1', '12.i1.a1', '12.i1.b1', '12.p1.a1', '12.r1.a1', '30.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7497, -1, 4732, -1, 8092, -1, 5134, -1], 'generators': [1, 480, 4, 192, 2, 488], 'label': '960.10116.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319860
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.56082', 'aut_weyl_index': 48, 'centralizer': '6.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.j1.a1', '12.k1.a1', '12.m1.a1', '12.n1.a1', '12.p1.a1', '12.v1.a1', '30.h1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5121, -1, 7482, -1, 6119, -1, 7050, -1], 'generators': [3, 480, 240, 192, 4, 488], 'label': '960.10116.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '24.14', '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': '2.1'}
  • id: 112319861
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 24, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.k1.a1', '12.l1.a1', '12.l1.b1', '12.r1.a1', '12.t1.a1', '12.t1.b1', '30.i1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7874, -1, 4817, -1, 7684, -1, 5721, -1], 'generators': [241, 480, 404, 192, 242, 488], 'label': '960.10116.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319862
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 24, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.o1.a1', '12.o1.b1', '12.q1.a1', '12.r1.a1', '12.w1.a1', '12.w1.b1', '30.j1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7307, -1, 4888, -1, 7842, -1, 5260, -1], 'generators': [5, 480, 240, 192, 6, 8], 'label': '960.10116.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.a1', 'projective_image': '24.14', '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': '4.2'}
  • id: 112319863
    {'ambient': '960.10116', 'aut_centralizer_order': 8, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 24, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '3.a1.a1'], 'contains': ['12.e1.a1', '12.p1.a1', '12.q1.a1', '12.s1.a1', '12.s1.b1', '12.u1.a1', '12.u1.b1', '30.k1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8774, -1, 7820, -1, 7967, -1, 7128, -1], 'generators': [241, 480, 4, 192, 242, 488], 'label': '960.10116.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.k1.a1', 'projective_image': '48.51', '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': '4.2'}
  • id: 112319864
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.c1.b1', '16.i1.a1', '16.m1.a1', '24.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2987, 5179, 5546, 6497, 1585, 3120, 4109, 5007], 'generators': [2, 480, 640, 488, 192], 'label': '960.10116.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.e1.a1', '4.d1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.c1.b1', '24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '48.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319865
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.b1.b1', '4.c1.b1', '4.d1.b1', '4.e1.b1', '4.f1.b1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.c1.c1', '16.c1.d1', '16.i1.b1', '16.m1.b1', '24.a1.b1', '40.a1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2987, 5179, 4334, 5985, 1585, 3120, 3963, 4795], 'generators': [1, 480, 640, 488, 192], 'label': '960.10116.8.a1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.a1.b1', '4.b1.b1', '4.c1.b1', '4.e1.b1', '4.d1.b1', '4.f1.b1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.d1', '16.c1.c1', '24.a1.b1', '40.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': '48.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319866
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.j1.b1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '16.j1.a1', '16.n1.a1', '24.g1.a1', '40.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1514, 4852, 5088, 4502, 1036, 5816, 3882, 6244], 'generators': [407, 480, 192, 488, 640], 'label': '960.10116.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.b1', '4.a1.a1', '4.h1.a1', '4.j1.a1', '4.j1.b1', '4.k1.a1', '4.i1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '48.51', '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': '12.4'}
  • id: 112319867
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['480.d1.c1', '480.d1.d1', '480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '4.t1.b1', '4.u1.b1', '4.v1.a1', '4.w1.a1', '6.e1.a1', '10.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2581, 4140, 5822, 6975, 3264, 6108, 6392, 2132], 'generators': [241, 480, 404, 192, 2, 640, 488], 'label': '960.10116.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '4.t1.b1', '4.u1.b1', '4.v1.a1', '4.w1.a1', '10.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '48.51', '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': '24.14'}
  • id: 112319868
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.b1.b1', '4.h1.a1', '4.l1.a1', '4.m1.a1', '4.n1.a1', '4.n1.b1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.h1.b1', '24.b1.a1', '40.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3245, 1755, 8285, 8724, 883, 4416, 9372, 846], 'generators': [488, 640, 192, 240, 480], 'label': '960.10116.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.b1', '4.b1.a1', '4.h1.a1', '4.l1.a1', '4.m1.a1', '4.n1.a1', '4.n1.b1'], 'normal_contains': ['16.a1.a1', '16.h1.b1', '16.h1.a1', '24.b1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 112319869
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '8.d1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.i1.a1', '4.l1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.e1.b1', '24.c1.a1', '40.d1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8483, 7431, 3453, 6310, 8366, 2695, 3805, 4552], 'generators': [3, 640, 192, 480, 488], 'label': '960.10116.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.g1.a1', '4.i1.a1', '4.l1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.b1', '16.e1.a1', '24.c1.a1', '40.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '48.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319870
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '8.e1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.b1', '4.j1.a1', '4.o1.a1', '4.s1.a1', '4.t1.a1', '4.u1.a1'], 'contains': ['16.a1.a1', '16.o1.a1', '24.d1.a1', '40.e1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2452, 3834, 8017, 7141, 1188, 3545, 7165, 1767], 'generators': [242, 640, 192, 488, 480], 'label': '960.10116.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1', '4.c1.b1', '4.j1.a1', '4.t1.a1', '4.s1.a1', '4.u1.a1', '4.o1.a1'], 'normal_contains': ['16.a1.a1', '24.d1.a1', '40.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '48.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319871
    {'ambient': '960.10116', 'aut_centralizer_order': 192, 'aut_label': '8.e1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.c1.a1', '4.j1.b1', '4.o1.a1', '4.s1.b1', '4.t1.b1', '4.u1.b1'], 'contains': ['16.a1.a1', '16.o1.b1', '24.d1.b1', '40.e1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2452, 3834, 7262, 8307, 1188, 3545, 7863, 1535], 'generators': [241, 640, 192, 488, 480], 'label': '960.10116.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.b1.b1', '4.c1.a1', '4.j1.b1', '4.t1.b1', '4.s1.b1', '4.u1.b1', '4.o1.a1'], 'normal_contains': ['16.a1.a1', '24.d1.b1', '40.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '48.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319872
    {'ambient': '960.10116', 'aut_centralizer_order': 384, 'aut_label': '8.f1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '32.45', 'aut_weyl_index': 384, 'centralizer': '4.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.c1.b1', '4.k1.a1', '4.l1.a1', '4.v1.a1', '4.w1.a1', '4.w1.b1'], 'contains': ['16.a1.a1', '16.k1.a1', '24.e1.a1', '40.f1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1922, 5924, 6740, 7553, 1312, 4862, 5418, 1304], 'generators': [731, 640, 192, 480, 8], 'label': '960.10116.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.c1.b1', '4.c1.a1', '4.k1.a1', '4.l1.a1', '4.v1.a1', '4.w1.a1', '4.w1.b1'], 'normal_contains': ['16.a1.a1', '24.e1.a1', '40.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '48.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 112319873
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '8.g1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.d1.b1', '4.k1.a1', '4.m1.a1', '4.p1.a1', '4.s1.a1', '4.s1.b1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.h1.a1', '40.g1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4927, 2246, 6802, 4848, 1889, 9429, 4865, 4670], 'generators': [4, 192, 8, 480, 640], 'label': '960.10116.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.d1.b1', '4.d1.a1', '4.k1.a1', '4.m1.a1', '4.s1.a1', '4.s1.b1', '4.p1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '40.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319874
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '8.h1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.e1.b1', '4.i1.a1', '4.m1.a1', '4.t1.a1', '4.t1.b1', '4.v1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.f1.b1', '24.i1.a1', '40.h1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5510, 5471, 5243, 5216, 3804, 6086, 4182, 5378], 'generators': [404, 192, 488, 480, 640], 'label': '960.10116.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.e1.b1', '4.e1.a1', '4.i1.a1', '4.m1.a1', '4.t1.a1', '4.t1.b1', '4.v1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.b1', '16.f1.a1', '40.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 112319875
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.e1.a1', '4.n1.a1', '4.q1.a1', '4.s1.a1', '4.u1.b1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '16.g1.c1', '24.j1.a1', '40.i1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5725, 4341, 5163, 5045, 3134, 4639, 3397, 5974], 'generators': [406, 192, 488, 480, 640], 'label': '960.10116.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.a1.b1', '4.e1.a1', '4.n1.a1', '4.s1.a1', '4.u1.b1', '4.w1.a1', '4.q1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.a1', '16.g1.c1', '40.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319876
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.e1.b1', '4.n1.b1', '4.q1.a1', '4.s1.b1', '4.u1.a1', '4.w1.b1'], 'contains': ['16.a1.a1', '16.g1.b1', '16.g1.d1', '24.j1.b1', '40.i1.b1'], 'core': '8.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5725, 4341, 4921, 4266, 3134, 4639, 4036, 6102], 'generators': [405, 192, 488, 480, 640], 'label': '960.10116.8.i1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.b1', 'normal_contained_in': ['4.a1.a1', '4.e1.b1', '4.n1.b1', '4.s1.b1', '4.u1.a1', '4.w1.b1', '4.q1.a1'], 'normal_contains': ['16.a1.a1', '16.g1.b1', '16.g1.d1', '40.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319877
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.b1', '4.j1.b1', '4.n1.a1', '4.r1.a1', '4.t1.a1', '4.w1.b1'], 'contains': ['16.a1.a1', '16.l1.a1', '24.k1.a1', '40.j1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3841, 3226, 6342, 7273, 2037, 6477, 5146, 3501], 'generators': [6, 192, 8, 480, 640], 'label': '960.10116.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.d1.a1', '4.f1.b1', '4.j1.b1', '4.n1.a1', '4.t1.a1', '4.w1.b1', '4.r1.a1'], 'normal_contains': ['16.a1.a1', '40.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319878
    {'ambient': '960.10116', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1536.408526562', 'aut_weyl_index': 8, 'centralizer': '24.b1.a1', 'complements': ['480.d1.a1', '480.d1.b1', '480.e1.a1', '480.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.e1.b1', '4.f1.b1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.b1', '6.e1.b1', '10.d1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2581, 4140, 7098, 6347, 3264, 6108, 6009, 3238], 'generators': [1, 480, 404, 192, 242, 640, 488], 'label': '960.10116.2.d1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.e1.b1', '4.f1.b1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.b1', '10.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319879
    {'ambient': '960.10116', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': 168, 'aut_stab_index': 2, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.f1.a1', '4.j1.a1', '4.n1.b1', '4.r1.a1', '4.t1.b1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.l1.b1', '24.k1.b1', '40.j1.b1'], 'core': '8.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3841, 3226, 4498, 7844, 2037, 6477, 5285, 2722], 'generators': [5, 192, 8, 480, 640], 'label': '960.10116.8.j1.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.b1', 'normal_contained_in': ['4.d1.b1', '4.f1.a1', '4.j1.a1', '4.n1.b1', '4.t1.b1', '4.w1.a1', '4.r1.a1'], 'normal_contains': ['16.a1.a1', '40.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319880
    {'ambient': '960.10116', 'aut_centralizer_order': 128, 'aut_label': '8.k1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.f1.b1', '4.h1.a1', '4.p1.a1', '4.u1.a1', '4.u1.b1', '4.v1.a1'], 'contains': ['16.a1.a1', '16.p1.a1', '24.l1.a1', '40.k1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1179, 2634, 7746, 6772, 747, 7595, 8253, 1994], 'generators': [7, 192, 480, 488, 640], 'label': '960.10116.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.f1.b1', '4.f1.a1', '4.h1.a1', '4.u1.a1', '4.u1.b1', '4.v1.a1', '4.p1.a1'], 'normal_contains': ['16.a1.a1', '40.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 112319881
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.a1', '4.x1.c1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.g1.b1', '24.o1.a1', '40.l1.a1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 437, 177, 7161, 1874, 712, 9384], 'generators': [405, 192, 488, 2, 640], 'label': '960.10116.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.a1.a1', '4.x1.c1', '4.x1.a1'], 'normal_contains': ['16.c1.a1', '16.d1.a1', '16.g1.b1', '40.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319882
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.b1', '4.x1.d1'], 'contains': ['16.c1.a1', '16.d1.b1', '16.g1.d1', '24.o1.b1', '40.l1.b1'], 'core': '8.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 924, 2370, 7161, 1874, 1172, 8006], 'generators': [885, 192, 488, 2, 640], 'label': '960.10116.8.l1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.b1', 'normal_contained_in': ['4.a1.a1', '4.x1.d1', '4.x1.b1'], 'normal_contains': ['16.c1.a1', '16.d1.b1', '16.g1.d1', '40.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.b1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319883
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.e1', '4.x1.g1'], 'contains': ['16.c1.b1', '16.d1.a1', '16.g1.d1', '24.o1.c1', '40.l1.c1'], 'core': '8.l1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 2530, 1863, 7161, 1874, 1702, 7189], 'generators': [885, 192, 488, 482, 640], 'label': '960.10116.8.l1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.c1', 'normal_contained_in': ['4.a1.a1', '4.x1.g1', '4.x1.e1'], 'normal_contains': ['16.c1.b1', '16.d1.a1', '16.g1.d1', '40.l1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.c1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319884
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.c1', '120.s1.d1', '120.m1.c1', '120.m1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.x1.f1', '4.x1.h1'], 'contains': ['16.c1.b1', '16.d1.b1', '16.g1.b1', '24.o1.d1', '40.l1.d1'], 'core': '8.l1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 254, 3306, 7161, 1874, 434, 9823], 'generators': [405, 192, 488, 482, 640], 'label': '960.10116.8.l1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.d1', 'normal_contained_in': ['4.a1.a1', '4.x1.h1', '4.x1.f1'], 'normal_contains': ['16.c1.b1', '16.d1.b1', '16.g1.b1', '40.l1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.d1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319885
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.x1.a1', '4.x1.e1'], 'contains': ['16.c1.c1', '16.d1.a1', '16.g1.a1', '24.o1.e1', '40.l1.e1'], 'core': '8.l1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 1679, 1500, 7161, 1874, 851, 8572], 'generators': [1, 192, 488, 406, 640], 'label': '960.10116.8.l1.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.e1', 'normal_contained_in': ['4.a1.b1', '4.x1.a1', '4.x1.e1'], 'normal_contains': ['16.c1.c1', '16.d1.a1', '16.g1.a1', '40.l1.e1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.e1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319886
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.x1.b1', '4.x1.f1'], 'contains': ['16.c1.c1', '16.d1.b1', '16.g1.c1', '24.o1.f1', '40.l1.f1'], 'core': '8.l1.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 866, 3429, 7161, 1874, 498, 8116], 'generators': [1, 192, 488, 886, 640], 'label': '960.10116.8.l1.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.f1', 'normal_contained_in': ['4.a1.b1', '4.x1.b1', '4.x1.f1'], 'normal_contains': ['16.c1.c1', '16.d1.b1', '16.g1.c1', '40.l1.f1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.f1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319887
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.x1.c1', '4.x1.g1'], 'contains': ['16.c1.d1', '16.d1.a1', '16.g1.c1', '24.o1.g1', '40.l1.g1'], 'core': '8.l1.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 2686, 54, 7161, 1874, 1499, 7896], 'generators': [481, 192, 488, 886, 640], 'label': '960.10116.8.l1.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.g1', 'normal_contained_in': ['4.a1.b1', '4.x1.c1', '4.x1.g1'], 'normal_contains': ['16.c1.d1', '16.d1.a1', '16.g1.c1', '40.l1.g1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.g1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 112319888
    {'ambient': '960.10116', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': 2, 'aut_stab_index': 8, 'aut_weyl_group': '96.206', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['120.s1.a1', '120.s1.b1', '120.m1.a1', '120.m1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.x1.d1', '4.x1.h1'], 'contains': ['16.c1.d1', '16.d1.b1', '16.g1.a1', '24.o1.h1', '40.l1.h1'], 'core': '8.l1.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [6719, 6816, 769, 924, 7161, 1874, 915, 9604], 'generators': [481, 192, 488, 406, 640], 'label': '960.10116.8.l1.h1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.l1.h1', 'normal_contained_in': ['4.a1.b1', '4.x1.d1', '4.x1.h1'], 'normal_contains': ['16.c1.d1', '16.d1.b1', '16.g1.a1', '40.l1.h1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.h1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}