Abstract group data - 1920.241003

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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': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 120, 'aut_gen_orders': [6, 6], 'aut_gens': [[27919159886133682205693581684409708745505149590404486637683112334133125594517609085134056889685846447838677034808754381, 24790072218381697593128049453294265561131986096342747340788549696417585749656911957001897096798573849909231407182278824], [3126978295166969399356290972744897373435686851033026637725135077040669511426776251952580451526002611978097461773648014, 37180739951289005407774805135815384610691129394860140895383393486411986215932393232937694325727766904141951275197609438], [32380962660422451380134654419517247360407643742253591212363860500613268059580985416283590385262443293085492934053519302, 18939947613544428296157635119449857185880994493340231377230707456666569794371357067448812519941302962322583786527477415]], 'aut_group': '1920.240996', 'aut_hash': 3616852219197380499, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 60, 'aut_perms': [2139472656889747555019285217382006518259612170342180377349044075325370646494788220, 6233189550174654501452864427253592705558487307206689023124830700491527013941602003], 'aut_phi_ratio': 3.75, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 1, 1], [3, 80, 1, 1], [4, 20, 1, 1], [4, 60, 1, 2], [4, 120, 1, 1], [5, 192, 2, 1], [6, 80, 1, 1], [6, 160, 2, 1], [8, 240, 1, 1], [10, 192, 2, 1], [12, 160, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:S_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '1920.240996', 'autcentquo_hash': 3616852219197380499, 'autcentquo_nilpotent': False, 'autcentquo_order': 1920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^4:S_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 10, 1], [3, 80, 1], [4, 20, 1], [4, 60, 2], [4, 120, 1], [5, 192, 2], [6, 80, 1], [6, 160, 2], [8, 240, 1], [10, 192, 2], [12, 160, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '960.11358', 'commutator_count': 2, 'commutator_label': '1920.241003', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '60.5'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 241003, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 1, 1], [3, 80, 1, 1], [4, 20, 1, 1], [4, 60, 1, 2], [4, 120, 1, 1], [5, 192, 2, 1], [6, 80, 1, 1], [6, 160, 2, 1], [8, 240, 1, 1], [10, 192, 2, 1], [12, 160, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1140, 'exponent': 120, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, -1, 1], [12, -1, 2], [16, -1, 1], [20, -1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '960.11358', 'hash': 241003, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [4, 5], 'inner_gens': [[27919159886133682205693581684409708745505149590404486637683112334133125594517609085134056889685846447838677034808754381, 49576519992431694490478816132365988545890484981771132192124259232536732257410580793641891540430437608749393325158292313], [47059548476961569899194094946999960403919812482797700187188956680806488435225506344682401160840686261441243981048127666, 24790072218381697593128049453294265561131986096342747340788549696417585749656911957001897096798573849909231407182278824]], 'inner_hash': 11358, 'inner_nilpotent': False, 'inner_order': 960, 'inner_split': True, 'inner_tex': 'C_2^4:A_5', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 4, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 1], [3, 2], [4, 2], [5, 4], [10, 2], [12, 2], [15, 1], [16, 1], [20, 2]], 'label': '1920.241003', 'linC_count': 1, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 8, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2.C2^4:A5', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 17, 'number_divisions': 14, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 73, 'number_subgroups': 2155, 'old_label': None, 'order': 1920, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 11], [3, 80], [4, 260], [5, 384], [6, 400], [8, 240], [10, 384], [12, 160]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [15720884250129057262839475205504241640465587979207806212666539071354428987653629440359141810217003292327394697751473421], 'outer_gens': [[36098555590795227262225670796319496540526898118023703051387324040888031292604976808526821674124639601956206140831032519, 42055226826840691130124137849487751840833428719595061134945514323669870652806901275879441493079230464343074697849389092]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 80, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 2], [5, 2], [6, 1], [10, 3], [15, 1], [16, 1], [20, 2], [24, 1]], 'representations': {'Perm': {'d': 80, 'gens': [27919159886133682205693581684409708745505149590404486637683112334133125594517609085134056889685846447838677034808754381, 24790072218381697593128049453294265561131986096342747340788549696417585749656911957001897096798573849909231407182278824]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2.C_2^4:A_5', 'transitive_degree': 80, '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: 109132918
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 241003, 'group_order': 1920, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109132927
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 241003, 'group_order': 1920, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 'size': 1}
  • id: 109132928
    {'aut_label': '2B', 'centralizer': '10.a1.a1', 'counter': 3, 'group_counter': 241003, 'group_order': 1920, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 'size': 10}
  • id: 109132929
    {'aut_label': '3A', 'centralizer': '80.a1.a1', 'counter': 4, 'group_counter': 241003, 'group_order': 1920, 'label': '3A', 'order': 3, 'powers': [4, 1, 4], 'representative': 18166639742277214876249578883676272388355176592552189116277776923553278078452808624850475302355315155645867709640187288, 'size': 80}
  • id: 109132930
    {'aut_label': '4A', 'centralizer': '20.a1.a1', 'counter': 5, 'group_counter': 241003, 'group_order': 1920, 'label': '4A', 'order': 4, 'powers': [2, 5, 5], 'representative': 17101720613026535683203701162363171139577591507039102303515362566643115299134217183983702886371253663024542800870928577, 'size': 20}
  • id: 109132931
    {'aut_label': '4B', 'centralizer': '60.c1.a1', 'counter': 6, 'group_counter': 241003, 'group_order': 1920, 'label': '4B', 'order': 4, 'powers': [3, 6, 6], 'representative': 57991206423025961787350489740212435435545713650821472918446132124287509826492238602105678420508442625261143795080341881, 'size': 60}
  • id: 109132932
    {'aut_label': '4C', 'centralizer': '60.c1.a1', 'counter': 7, 'group_counter': 241003, 'group_order': 1920, 'label': '4C', 'order': 4, 'powers': [3, 7, 7], 'representative': 53694650137434997219312725565052629768828732453146181953203755648525379630742965611620272344157194460340953142949706663, 'size': 60}
  • id: 109132933
    {'aut_label': '4D', 'centralizer': '120.g1.a1', 'counter': 8, 'group_counter': 241003, 'group_order': 1920, 'label': '4D', 'order': 4, 'powers': [2, 8, 8], 'representative': 15720883463978770255130336140943350007948943708394147108532588248634676370041655776980938111336676879742642224177644027, 'size': 120}
  • id: 109132934
    {'aut_label': '5A1', 'centralizer': '192.a1.a1', 'counter': 9, 'group_counter': 241003, 'group_order': 1920, 'label': '5A1', 'order': 5, 'powers': [10, 10, 1], 'representative': 45225193693604378506908506190053963977682271876290895151966004086005410186495416479424297593735214338664411110457986600, 'size': 192}
  • id: 109132919
    {'aut_label': '5A1', 'centralizer': '192.a1.a1', 'counter': 10, 'group_counter': 241003, 'group_order': 1920, 'label': '5A2', 'order': 5, 'powers': [9, 9, 1], 'representative': 19744425021034190223382422324311597486018759191259266114226282693814388257481654776995541558579779057899290240601079330, 'size': 192}
  • id: 109132920
    {'aut_label': '6A', 'centralizer': '80.a1.a1', 'counter': 11, 'group_counter': 241003, 'group_order': 1920, 'label': '6A', 'order': 6, 'powers': [4, 2, 11], 'representative': 59459131181257542303651650115318094388140299332232546110536705248820567029391049766730530302252780320362176397395851008, 'size': 80}
  • id: 109132921
    {'aut_label': '6B1', 'centralizer': '160.a1.a1', 'counter': 12, 'group_counter': 241003, 'group_order': 1920, 'label': '6B1', 'order': 6, 'powers': [4, 3, 13], 'representative': 13138400776767501243809780724198950420380306440804765267890563423256962425497021670360001043912483709855774722969631276, 'size': 160}
  • id: 109132922
    {'aut_label': '6B1', 'centralizer': '160.a1.a1', 'counter': 13, 'group_counter': 241003, 'group_order': 1920, 'label': '6B-1', 'order': 6, 'powers': [4, 3, 12], 'representative': 18347813333162227613616228212414157898730539631300914317349646436557020605884196313031474189033999631553785936270033931, 'size': 160}
  • id: 109132923
    {'aut_label': '8A', 'centralizer': '240.f1.a1', 'counter': 14, 'group_counter': 241003, 'group_order': 1920, 'label': '8A', 'order': 8, 'powers': [5, 14, 14], 'representative': 34758891198070211081843531450241176420146398001422448121606568622514627610819794187436824064904759121318408772694463576, 'size': 240}
  • id: 109132924
    {'aut_label': '10A1', 'centralizer': '192.a1.a1', 'counter': 15, 'group_counter': 241003, 'group_order': 1920, 'label': '10A1', 'order': 10, 'powers': [9, 16, 2], 'representative': 26489008425355785316848807925440990334695162037745368928580099026696698136307920596934835091955054174144990164792026047, 'size': 192}
  • id: 109132925
    {'aut_label': '10A1', 'centralizer': '192.a1.a1', 'counter': 16, 'group_counter': 241003, 'group_order': 1920, 'label': '10A3', 'order': 10, 'powers': [10, 15, 2], 'representative': 65938954953805579327017887546819468633160817742329180913034075161242047597350843056150547835954773981536469771613089922, 'size': 192}
  • id: 109132926
    {'aut_label': '12A', 'centralizer': '160.b1.a1', 'counter': 17, 'group_counter': 241003, 'group_order': 1920, 'label': '12A', 'order': 12, 'powers': [11, 5, 17], 'representative': 53110293898427689323995535019025447479689133390163108510633405198199996324291437648116535450589557126271222358521147989, 'size': 160}
• 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: 4154758
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.1a', '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], 'schur_index': 1}
  • id: 4154765
    {'cdim': 4, 'counter': 3, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.4a', 'multiplicity': 1, 'nt': [5, 4], 'qdim': 4, 'qvalues': [4, 4, 4, 1, 4, 0, 0, 0, -1, -1, 1, 1, 1, 0, -1, -1, 1], 'schur_index': 1}
  • id: 4154766
    {'cdim': 4, 'counter': 4, 'faithful': True, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.4b', 'multiplicity': 1, 'nt': [240, 0], 'qdim': 4, 'qvalues': [4, -4, 0, -2, 0, -2, 2, 0, -1, -1, 2, 0, 0, 0, 1, 1, 0], 'schur_index': 2}
  • id: 4154767
    {'cdim': 5, 'counter': 5, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.5a', 'multiplicity': 1, 'nt': [6, 12], 'qdim': 5, 'qvalues': [5, 5, 5, -1, 5, 1, 1, 1, 0, 0, -1, -1, -1, 1, 0, 0, -1], 'schur_index': 1}
  • id: 4154768
    {'cdim': 5, 'counter': 6, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.5b', 'multiplicity': 1, 'nt': [10, 34], 'qdim': 5, 'qvalues': [5, 5, -3, 2, 1, 1, 1, 1, 0, 0, 2, 0, 0, -1, 0, 0, -2], 'schur_index': 1}
  • id: 4154764
    {'cdim': 3, 'counter': 2, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.3a', 'multiplicity': 2, 'nt': [12, 33], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 6, -2, -2, -2, 1, 1, 0, 0, 0, -2, 1, 1, 0], 'schur_index': 1}
  • id: 4154769
    {'cdim': 5, 'counter': 7, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.5c', 'multiplicity': 2, 'nt': [30, 217], 'qdim': 10, 'qvalues': [10, 10, -6, -2, 2, 2, 2, 2, 0, 0, -2, 0, 0, -2, 0, 0, 2], 'schur_index': 1}
  • id: 4154770
    {'cdim': 10, 'counter': 8, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.10a', 'multiplicity': 1, 'nt': [16, 1081], 'qdim': 10, 'qvalues': [10, 10, 2, 1, -2, -2, -2, 2, 0, 0, 1, -1, -1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 4154771
    {'cdim': 10, 'counter': 9, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.10b', 'multiplicity': 1, 'nt': [20, 177], 'qdim': 10, 'qvalues': [10, 10, 2, 1, -2, 2, 2, -2, 0, 0, 1, -1, -1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 4154760
    {'cdim': 15, 'counter': 11, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.15a', 'multiplicity': 1, 'nt': [30, 214], 'qdim': 15, 'qvalues': [15, 15, -9, 0, 3, -1, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
  • id: 4154761
    {'cdim': 16, 'counter': 12, 'faithful': True, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.16a', 'multiplicity': 1, 'nt': [240, 0], 'qdim': 16, 'qvalues': [16, -16, 0, -2, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, -1, -1, 0], 'schur_index': 2}
  • id: 4154762
    {'cdim': 20, 'counter': 13, 'faithful': False, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.20a', 'multiplicity': 1, 'nt': [40, 942], 'qdim': 20, 'qvalues': [20, 20, 4, -1, -4, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, -1], 'schur_index': 1}
  • id: 4154763
    {'cdim': 20, 'counter': 14, 'faithful': True, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.20b', 'multiplicity': 1, 'nt': [80, 0], 'qdim': 20, 'qvalues': [20, -20, 0, 2, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 4154759
    {'cdim': 12, 'counter': 10, 'faithful': True, 'group': '1920.241003', 'group_order': 1920, 'image': None, 'label': '1920.241003.12a', 'multiplicity': 2, 'nt': [240, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 4, -4, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0], 'schur_index': 2}
• 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: 6040615
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1920, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1920, 'label': '1920.241003.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6040624
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 2, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241003.3a1', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 6040625
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 3, 'cyclotomic_n': 5, 'dim': 3, 'faithful': False, 'field': [-1, -1, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241003.3a2', 'nt': [12, 33], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]]]}
  • id: 6040626
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 4, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241003.4a', 'nt': [5, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 6040627
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 5, 'cyclotomic_n': 1, 'dim': 4, 'faithful': True, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241003', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241003.4b', 'nt': [240, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 6040628
    {'center': '60.a1.a1', 'center_index': 60, 'center_order': 32, 'counter': 6, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '60.5', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 32, 'label': '1920.241003.5a', 'nt': [6, 12], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 6040629
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 7, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.5b', 'nt': [10, 34], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 6040630
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 8, 'cyclotomic_n': 3, 'dim': 5, 'faithful': False, 'field': [1, -1, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.5c1', 'nt': [30, 217], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040631
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 9, 'cyclotomic_n': 3, 'dim': 5, 'faithful': False, 'field': [1, -1, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 0, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.5c2', 'nt': [30, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040616
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 10, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.10a', 'nt': [16, 1081], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040617
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 11, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.10b', 'nt': [20, 177], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 6040618
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 12, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241003', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241003.12a1', 'nt': [240, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]]]}
  • id: 6040619
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 13, 'cyclotomic_n': 5, 'dim': 12, 'faithful': True, 'field': [-1, -1, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241003', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241003.12a2', 'nt': [240, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 6040620
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 14, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.15a', 'nt': [30, 214], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-9, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 6040621
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241003', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241003.16a', 'nt': [240, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 6040622
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '960.11358', 'image_order': 960, 'indicator': 1, 'kernel': '960.a1.a1', 'kernel_order': 2, 'label': '1920.241003.20a', 'nt': [40, 942], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[4, 0]], [[-1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 6040623
    {'center': '960.a1.a1', 'center_index': 960, 'center_order': 2, 'counter': 17, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '1920.241003', 'group_counter': 241003, 'group_order': 1920, 'image': None, 'image_isoclass': '1920.241003', 'image_order': 1920, 'indicator': -1, 'kernel': '1920.a1.a1', 'kernel_order': 1, 'label': '1920.241003.20b', 'nt': [80, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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: 63520823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1920, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '1920.241003.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': False, 'special_labels': ['D', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1920.241003', 'subgroup_hash': 2145338050002567253, 'subgroup_order': 1920, 'subgroup_tex': 'C_2.C_2^4:A_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1920.241003.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.618', 'subgroup_hash': 618, 'subgroup_order': 384, 'subgroup_tex': 'Q_8^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 63520845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.6.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '320.1581', 'subgroup_hash': 1581, 'subgroup_order': 320, 'subgroup_tex': 'C_2.C_2^4:D_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1022', 'subgroup_hash': 1022, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.10.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.989', 'subgroup_hash': 989, 'subgroup_order': 192, 'subgroup_tex': 'D_4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '160.199', 'subgroup_hash': 199, 'subgroup_order': 160, 'subgroup_tex': 'C_2.C_2^4:C_5', 'supersolvable': False, 'sylow': 0}
  • id: 63520889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1920.241003.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '128.937', 'subgroup_hash': 937, 'subgroup_order': 128, 'subgroup_tex': 'Q_8\\wr C_2', 'supersolvable': True, 'sylow': 2}
  • id: 63520894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.16.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
  • id: 63520895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.67', 'subgroup_hash': 67, 'subgroup_order': 96, 'subgroup_tex': '\\Unitary(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.191', 'subgroup_hash': 191, 'subgroup_order': 96, 'subgroup_tex': 'C_4.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.202', 'subgroup_hash': 202, 'subgroup_order': 96, 'subgroup_tex': 'D_4.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.37', 'subgroup_hash': 37, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.30.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': '64.239', 'subgroup_hash': 239, 'subgroup_order': 64, 'subgroup_tex': 'Q_8^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.30.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': '64.137', 'subgroup_hash': 137, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 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': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63520833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 63520835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.28', 'subgroup_hash': 28, 'subgroup_order': 48, 'subgroup_tex': 'C_2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 63520836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1920.241003.60.a1.a1', 'maximal': False, 'maximal_normal': True, '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': '60.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'A_5', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.50', 'subgroup_hash': 50, 'subgroup_order': 32, 'subgroup_tex': 'C_4.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 63520837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.8', 'subgroup_hash': 8, 'subgroup_order': 32, 'subgroup_tex': 'C_4.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.60.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': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.60.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': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520846
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 63520850
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 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': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.a1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1.a2', 'outer_equivalence': False, 'perfect': False, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63520857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.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': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63520863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 63520864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.120.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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
  • id: 63520865
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63520866
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 63520868
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520869
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': 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: 63520870
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520875
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.240.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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.240.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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 63520881
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63520882
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 63520883
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '1920.241003.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.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': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 63520884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1920.241003.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 63520885
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520886
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 63520887
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.480.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63520888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.480.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 63520890
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '1920.241003.640.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '640.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': 640, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
  • id: 63520891
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1920, 'characteristic': True, 'core_order': 2, 'counter': 71, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1920.241003.960.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '960.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '960.11358', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11358, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 960, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:A_5', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'S', 'U0', 'C2'], '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: 63520892
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1920.241003.960.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '960.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 63520893
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1920.241003', 'ambient_counter': 241003, 'ambient_order': 1920, 'ambient_tex': 'C_2.C_2^4:A_5', 'central': True, 'central_factor': False, 'centralizer_order': 1920, 'characteristic': True, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1920.241003.1920.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1920.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1920.241003', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2145338050002567253, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1920, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2.C_2^4:A_5', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C3'], '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: 63520823
    {'ambient': '1920.241003', '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': '960.a1.a1', 'complements': ['1920.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['5.a1.a1', '6.a1.a1', '10.b1.a1', '16.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7025, 5000, 5236, 5000, 8413, 5000, 1683, 5000], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 15165269849086195961190616024312611043802853554318974853792791318280628132001921388518420123643894082257584878020771885, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 906682211426110278482291418023757106932803422521952317206829887740519517272760662798058216768949828160310084339595040, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '960.11358', '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': '960.11358'}
  • id: 63520824
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 10, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.e1.a1', '40.f1.a1', '60.g1.a1', '80.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8701, -1, 7776, -1, 8066, -1, 1963, -1], 'generators': [27919159886133682205693581684409708745505149590404486637683112334133125594517609085134056889685846447838677034808754381, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 4565305277370936543789577000308551869517291372910520275731418673582902614980390342313327926377221549102832122399233003, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 63520825
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 10, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '10.b1.a1'], 'contains': ['40.a1.a1', '40.e1.a1', '60.a1.a1', '80.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6491, -1, 6144, -1, 7071, -1, 3011, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.c1.a1', 'projective_image': '960.11358', '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': '96.195'}
  • id: 63520826
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.928', 'aut_weyl_index': 15, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.d1.a1', '60.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3650, -1, 3776, -1, 5072, -1, 4902, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
  • id: 63520827
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.955', 'aut_weyl_index': 10, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.c1.a1', '60.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2577, -1, 2847, -1, 3096, -1, 7256, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 64794336840188909339027427788176500537571888338947598797003882427265473255531576056397431104194200860162816843427010197, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '960.11358', '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': '96.70'}
  • id: 63520828
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.928', 'aut_weyl_index': 15, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.d1.a1', '60.e1.a1', '60.f1.a1', '60.g1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5603, -1, 7098, -1, 6131, -1, 3885, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '960.11358', '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': '64.138'}
  • id: 63520829
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '20.c1.a1'], 'contains': ['80.d1.a1', '120.e1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [4524, -1, 5377, -1, 4285, -1, 5657, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.40.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1.a1', 'old_label': '40.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 63520830
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.f1.a1', '120.h1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1105, -1, 733, -1, 768, -1, 9156, -1], 'generators': [34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 66289841429114458251661940245469505153987483175396978279102344394856790155691216444355676337971040928340311792825981386, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872, 49293418623101595405938605219069915167872337233134657159733808100363855209415059371780551046225032982299840478056510918], 'label': '1920.241003.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '960.11358', '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': '12.3'}
  • id: 63520831
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['80.e1.a1', '120.i1.a1', '160.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2885, -1, 2919, -1, 2888, -1, 6585, -1], 'generators': [69291092727901077522599166639006541397065209326049451167317807644462328689534904161276410563576571809023150876180177710, 52268311189321328495110950665351209042140974748832422966762431863997046937351545248808357558183213930678168093791378881, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.40.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '40.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520832
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '48.38', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '80.c1.a1', '120.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9099, -1, 9447, -1, 8755, -1, 1368, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 8213937762155300482264099928462107610008134666291091205819075447790378936490591916359044349074658554641939744103969371, 9954479007471677975224621024433404466795266383443395141582676284369415188354624897685777606627082421542308221822581230, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '40.d1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 63520833
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.d1.a1', '120.k1.a1', '160.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6676, -1, 8658, -1, 7654, -1, 2424, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 43364168849893177994317419243360413369471361225931317491792890779239384180670195850132954834031486659029992346497125966], 'label': '1920.241003.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '40.e1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63520834
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.5602', 'aut_weyl_index': 5, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '15.a1.a1', '20.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4796, -1, 4465, -1, 6506, -1, 3770, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '192.201'}
  • id: 63520835
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.d1.a1', '120.l1.a1', '160.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9878, -1, 8215, -1, 8135, -1, 1963, -1], 'generators': [27919159886133682205693581684409708745505149590404486637683112334133125594517609085134056889685846447838677034808754381, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.40.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.f1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
  • id: 63520836
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240996', 'aut_weyl_index': 1, 'centralizer': '960.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.c1.a1', '30.c1.a1'], 'contains': ['120.e1.a1', '120.k1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5471, 5000, 6545, 5000, 6344, 5000, 3681, 5000], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': -60, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '960.11358'}
  • id: 63520837
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '32.27', 'aut_weyl_index': 60, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1'], 'contains': ['120.a1.a1', '120.a1.a2', '120.c1.a1', '120.f1.a1', '120.g1.a1', '120.i1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2324, -1, 2053, -1, 2189, -1, 7664, -1], 'generators': [4848567017276856517185471762875367232731724043852309091350348342923496701931738320595265435888756882804910687500592649, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 39762863826081114175898041318731541995042257140902220792108816816459393454147677468628378920253070009691262538691371605, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 38556384939170334346565726857727595198356243772617431040257379586769763419250436639487551658867727335119162735646428046], 'label': '1920.241003.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.b1.a1', 'projective_image': '960.11358', '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': '16.14'}
  • id: 63520838
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1'], 'contains': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.f1.a1', '120.g1.a1', '120.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1255, -1, 1406, -1, 1657, -1, 8175, -1], 'generators': [4848567017276856517185471762875367232731724043852309091350348342923496701931738320595265435888756882804910687500592649, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 38556384939170334346565726857727595198356243772617431040257379586769763419250436639487551658867727335119162735646428046], 'label': '1920.241003.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '960.11358', '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': '8.5'}
  • id: 63520839
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.138', 'aut_weyl_index': 30, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.c1.a1', '120.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3447, -1, 3600, -1, 3586, -1, 7256, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 64794336840188909339027427788176500537571888338947598797003882427265473255531576056397431104194200860162816843427010197, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 63520840
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '128.928', 'aut_weyl_index': 15, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.a1'], 'contains': ['120.d1.a1', '120.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4919, -1, 5697, -1, 5072, -1, 4902, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '960.11358', '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': '64.138'}
  • id: 63520841
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '30.c1.a1'], 'contains': ['120.b1.a1', '120.d1.a1', '120.k1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [6073, -1, 7661, -1, 5729, -1, 4272, -1], 'generators': [4565305277370936543789577000308551869517291372910520275731418673582902614980390342313327926377221549102832122399233003, 64794336840188909339027427788176500537571888338947598797003882427265473255531576056397431104194200860162816843427010197, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 14406393862864307400550582307622461018351230337987088187873239590009869536664751503039103284275244783229196604154161600], 'label': '1920.241003.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.f1.a1', 'projective_image': '960.11358', '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': '16.11'}
  • id: 63520866
    {'ambient': '1920.241003', 'aut_centralizer_order': 12, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '160.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1.a1', '80.a1.a1', '80.b1.a1', '80.c1.a1'], 'contains': ['320.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7528, -1, 9596, -1, 7876, -1, 1812, -1], 'generators': [17101720613026535683203701162363171139577591507039102303515362566643115299134217183983702886371253663024542800870928577, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 43364168849893177994317419243360413369471361225931317491792890779239384180670195850132954834031486659029992346497125966], 'label': '1920.241003.160.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '160.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520842
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '64.226', 'aut_weyl_index': 30, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '30.c1.a1'], 'contains': ['120.c1.a1', '120.d1.a1', '120.j1.a1', '120.k1.a1', '120.l1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [7927, -1, 7060, -1, 6904, -1, 3144, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 4565305277370936543789577000308551869517291372910520275731418673582902614980390342313327926377221549102832122399233003, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 14406393862864307400550582307622461018351230337987088187873239590009869536664751503039103284275244783229196604154161600], 'label': '1920.241003.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '60.g1.a1', 'projective_image': '960.11358', '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': '32.27'}
  • id: 63520843
    {'ambient': '1920.241003', 'aut_centralizer_order': 3, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '320.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '40.d1.a1'], 'contains': ['160.a1.a1', '160.b1.a1', '240.d1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7220, -1, 7814, -1, 7464, -1, 2433, -1], 'generators': [17101720613026535683203701162363171139577591507039102303515362566643115299134217183983702886371253663024542800870928577, 4565305277370936543789577000308551869517291372910520275731418673582902614980390342313327926377221549102832122399233003, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527], 'label': '1920.241003.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 63520844
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '48.38', 'aut_weyl_index': 40, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '40.d1.a1'], 'contains': ['160.b1.a1', '160.c1.a1', '240.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9534, -1, 9157, -1, 9227, -1, 910, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9954479007471677975224621024433404466795266383443395141582676284369415188354624897685777606627082421542308221822581230, 25107151984105074729786904179271878119551341166250965245207153066369354968121460209051997168510137589775740904871995887, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 63520845
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '320.1635', 'aut_weyl_index': 6, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '30.c1.a1', '96.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6106, -1, 6425, -1, 8843, -1, 1155, -1], 'generators': [32279025076537209958245527310008417993011626683287199735162127962306528114043151491053460143456309251129114458163026262, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 66765491426108291934825827112769003338695133308510323685362813128037521662009012957977125350915776987754504049046820280, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.6.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '160.234'}
  • id: 63520846
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.4', 'aut_weyl_index': 160, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '40.d1.a1'], 'contains': ['160.b1.a1', '240.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [8945, -1, 9885, -1, 8802, -1, 1319, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 32267683385268895723166186548206665575282358305089364862463042964446763588176189665161531012640102757613483354244117227, 9954479007471677975224621024433404466795266383443395141582676284369415188354624897685777606627082421542308221822581230, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '80.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63520847
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.e1.a1', '40.f1.a1'], 'contains': ['240.g1.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5634, -1, 8615, -1, 6534, -1, 3326, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 46006712971394263180784344539267020918684943606571499857092863145740169214659963765057870264649117915146808982816516231, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.80.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '80.d1.a1', 'projective_image': '960.11358', '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': '24.12'}
  • id: 63520848
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.c1.a1'], 'contains': ['240.h1.a1', '320.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [6024, -1, 4261, -1, 4609, -1, 4560, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 55884456014391293384730753914733949351573911683448264028854538965382017601191821249314540959616522798947600128519451712, 46006712971394263180784344539267020918684943606571499857092863145740169214659963765057870264649117915146808982816516231, 40663359100977769837324007533876423432026715848035751477861532967440749059883483145070915697270193579149825976164379873], 'label': '1920.241003.80.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '80.e1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 63520849
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1'], 'contains': ['240.j1.a1', '320.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [544, -1, 298, -1, 157, -1, 9849, -1], 'generators': [54593569438571673023572183920701744371410899249788967840711683295379597650012246039095251586650046032085321109014207003, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 63537184167314187920863286038136291853601699165718856399969194118831573619889462320271337812889349573745390532166441433, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.80.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.b1.a1', 'old_label': '80.f1.a1', 'projective_image': '1920.241003', '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': '12.3'}
  • id: 63520850
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '20.3', 'aut_weyl_index': 96, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '16.a1.a1'], 'contains': ['192.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [7863, -1, 4896, -1, 9829, -1, 164, -1], 'generators': [6692807047081603735381337681247553688365657623132087261734896012213039700704510199399615858603426281946145940116641793, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 38952757332387419753758549758338309610865613344096814160593132343787395799676174945100402361407873912227702699624351970], 'label': '1920.241003.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 63520851
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.5', 'aut_weyl_index': 240, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1780, -1, 2723, -1, 2189, -1, 7899, -1], 'generators': [4848567017276856517185471762875367232731724043852309091350348342923496701931738320595265435888756882804910687500592649, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 38556384939170334346565726857727595198356243772617431040257379586769763419250436639487551658867727335119162735646428046], 'label': '1920.241003.120.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63520852
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.5', 'aut_weyl_index': 240, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '60.d1.a1'], 'contains': ['240.a1.a1', '240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1780, -1, 1742, -1, 2189, -1, 7491, -1], 'generators': [56722999291074885194189624989821764269303248619773962638666513498903126723169500651032827774093992317794983556560345951, 14700957333789223662364704237908767732470438502284476212617514545636978892955824571697034553753501420477757208507460323, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.120.a1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.a1.a2', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63520853
    {'ambient': '1920.241003', 'aut_centralizer_order': 16, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.d1.a1', '60.f1.a1'], 'contains': ['240.a1.a1', '240.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3143, -1, 3417, -1, 3406, -1, 7105, -1], 'generators': [64794336840188909339027427788176500537571888338947598797003882427265473255531576056397431104194200860162816843427010197, 34373871739604867957900400953812505184408940242126637578726538682083792654248833324493571631698012744850569356706429469, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304], 'label': '1920.241003.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 63520854
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.138', 'aut_weyl_index': 30, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3642, -1, 4209, -1, 3915, -1, 6008, -1], 'generators': [56722999291074885194189624989821764269303248619773962638666513498903126723169500651032827774093992317794983556560345951, 34373871739604867957900400953812505184408940242126637578726538682083792654248833324493571631698012744850569356706429469, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304], 'label': '1920.241003.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
  • id: 63520855
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.e1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '240.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5321, -1, 6306, -1, 5678, -1, 4147, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 34373871739604867957900400953812505184408940242126637578726538682083792654248833324493571631698012744850569356706429469, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304], 'label': '1920.241003.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.c1.a1', 'old_label': '120.d1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
  • id: 63520856
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.955', 'aut_weyl_index': 10, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.b1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2853, -1, 3106, -1, 3378, -1, 6585, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 64794336840188909339027427788176500537571888338947598797003882427265473255531576056397431104194200860162816843427010197, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.10.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63520857
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.955', 'aut_weyl_index': 10, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '60.a1.a1', '60.d1.a1', '60.e1.a1'], 'contains': ['240.a1.a1', '240.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4439, -1, 5283, -1, 5127, -1, 5058, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '120.e1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '96.70'}
  • id: 63520858
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '240.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1'], 'contains': ['240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [991, -1, 1351, -1, 1208, -1, 8672, -1], 'generators': [69291092727901077522599166639006541397065209326049451167317807644462328689534904161276410563576571809023150876180177710, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.f1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 63520859
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1'], 'contains': ['240.b1.a1', '240.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1386, -1, 980, -1, 1786, -1, 8286, -1], 'generators': [59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 66289841429114458251661940245469505153987483175396978279102344394856790155691216444355676337971040928340311792825981386, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '120.g1.a1', 'projective_image': '960.11358', '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': '4.2'}
  • id: 63520860
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '120.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '120.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '60.c1.a1'], 'contains': ['240.b1.a1', '240.i1.a1', '240.j1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [299, -1, 349, -1, 676, -1, 9352, -1], 'generators': [66289841429114458251661940245469505153987483175396978279102344394856790155691216444355676337971040928340311792825981386, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872, 49293418623101595405938605219069915167872337233134657159733808100363855209415059371780551046225032982299840478056510918], 'label': '1920.241003.120.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.h1.a1', 'projective_image': '960.11358', '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': '12.3'}
  • id: 63520861
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '120.i1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '96.227', 'aut_weyl_index': 20, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '60.b1.a1'], 'contains': ['240.c1.a1', '240.h1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2472, -1, 2233, -1, 2721, -1, 6616, -1], 'generators': [69291092727901077522599166639006541397065209326049451167317807644462328689534904161276410563576571809023150876180177710, 52268311189321328495110950665351209042140974748832422966762431863997046937351545248808357558183213930678168093791378881, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.120.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.i1.a1', 'projective_image': '960.11358', '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': '48.50'}
  • id: 63520862
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '120.j1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '60.g1.a1'], 'contains': ['240.d1.a1', '240.e1.a1', '240.f1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8638, -1, 8487, -1, 8010, -1, 1909, -1], 'generators': [34373871739604867957900400953812505184408940242126637578726538682083792654248833324493571631698012744850569356706429469, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 70991911134707636448269982938312382746290227285030929765029806333485167255963030492236190585441753055717080418778807390], 'label': '1920.241003.120.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '120.j1.a1', 'projective_image': '960.11358', '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': '16.11'}
  • id: 63520863
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '120.k1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.e1.a1', '60.a1.a1', '60.f1.a1', '60.g1.a1'], 'contains': ['240.a1.a1', '240.d1.a1', '240.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6667, -1, 6949, -1, 6122, -1, 3721, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775], 'label': '1920.241003.120.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '120.k1.a1', 'projective_image': '960.11358', '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': '48.48'}
  • id: 63520864
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '120.l1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '16.11', 'aut_weyl_index': 120, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.f1.a1', '60.g1.a1'], 'contains': ['240.e1.a1', '240.f1.a1', '240.g1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [9063, -1, 7926, -1, 6941, -1, 2935, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 14406393862864307400550582307622461018351230337987088187873239590009869536664751503039103284275244783229196604154161600], 'label': '1920.241003.120.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '120.l1.a1', 'projective_image': '960.11358', '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': '16.11'}
  • id: 63520865
    {'ambient': '1920.241003', 'aut_centralizer_order': 6, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.b1.a1', '40.c1.a1', '80.a1.a1'], 'contains': ['320.a1.a1', '320.b1.a1', '480.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [3863, -1, 3456, -1, 4137, -1, 5639, -1], 'generators': [34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520867
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 10, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '30.c1.a1', '40.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7233, -1, 7729, -1, 7686, -1, 2407, -1], 'generators': [27919159886133682205693581684409708745505149590404486637683112334133125594517609085134056889685846447838677034808754381, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.10.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '10.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.195'}
  • id: 63520868
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '12.4', 'aut_weyl_index': 160, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.f1.a1', '80.b1.a1'], 'contains': ['320.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [9728, -1, 6434, -1, 8501, -1, 910, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 32380962487558593309053315215376942922040187044374622159933034502448563867963406888535455571176840492815637871456845672, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.160.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '80.b1.a1', 'old_label': '160.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 63520869
    {'ambient': '1920.241003', 'aut_centralizer_order': 5, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '96.a1.a1'], 'contains': ['384.a1.a1', '960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6780, -1, 5194, -1, 9643, -1, 209, -1], 'generators': [32279025076537209958245527310008417993011626683287199735162127962306528114043151491053460143456309251129114458163026262, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527], 'label': '1920.241003.192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520870
    {'ambient': '1920.241003', 'aut_centralizer_order': 16, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.k1.a1'], 'contains': ['480.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4597, -1, 4248, -1, 5118, -1, 5035, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669], 'label': '1920.241003.240.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 63520871
    {'ambient': '1920.241003', 'aut_centralizer_order': 32, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '60.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.a2', '120.b1.a1', '120.f1.a1', '120.g1.a1', '120.h1.a1'], 'contains': ['480.a1.a1', '480.d1.a1', '480.e1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1386, -1, 1397, -1, 1939, -1, 7899, -1], 'generators': [66289841429114458251661940245469505153987483175396978279102344394856790155691216444355676337971040928340311792825981386, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.240.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520872
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.a1.a2', '120.c1.a1', '120.f1.a1', '120.g1.a1', '120.i1.a1'], 'contains': ['480.a1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2472, -1, 2492, -1, 2721, -1, 6958, -1], 'generators': [69291092727901077522599166639006541397065209326049451167317807644462328689534904161276410563576571809023150876180177710, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 63520873
    {'ambient': '1920.241003', 'aut_centralizer_order': 24, 'aut_label': '240.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '80.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '120.j1.a1', '120.k1.a1'], 'contains': ['480.a1.a1', '480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7581, -1, 7806, -1, 6710, -1, 3131, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 3659215396961680490890844530218548054024787043389450088995135291714570798678192457266412015173622362223741559866610810], 'label': '1920.241003.240.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '240.d1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 63520874
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '240.e1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.b1.a1', '120.c1.a1', '120.j1.a1', '120.l1.a1'], 'contains': ['480.b1.a1', '480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8868, -1, 8130, -1, 7376, -1, 2491, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 70199211452257123155138014151243499201035846024057735542553471052138733267303391197888113402400890357704978614329026089, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304], 'label': '1920.241003.240.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '240.e1.a1', 'projective_image': '960.11358', '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': '8.3'}
  • id: 63520875
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '240.f1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '4.2', 'aut_weyl_index': 480, 'centralizer': '240.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a1', '120.d1.a1', '120.j1.a1', '120.l1.a1'], 'contains': ['480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [8329, -1, 8786, -1, 7043, -1, 2811, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304], 'label': '1920.241003.240.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.g1.a1', 'old_label': '240.f1.a1', 'projective_image': '960.11358', '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': '4.2'}
  • id: 63520876
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '240.g1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '240.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.d1.a1', '120.e1.a1', '120.k1.a1', '120.l1.a1'], 'contains': ['480.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6395, -1, 7491, -1, 6201, -1, 3450, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304], 'label': '1920.241003.240.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '240.g1.a1', 'projective_image': '960.11358', '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': '24.12'}
  • id: 63520877
    {'ambient': '1920.241003', 'aut_centralizer_order': 2, 'aut_label': '240.h1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '480.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1.a1', '120.i1.a1'], 'contains': ['480.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [5214, -1, 3643, -1, 4618, -1, 4316, -1], 'generators': [52268311189321328495110950665351209042140974748832422966762431863997046937351545248808357558183213930678168093791378881, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 53189539277594972130754827999485283529017066398448821003944801026637096415522484289350368768379552071545917405651447366], 'label': '1920.241003.240.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.c1.a1', 'old_label': '240.h1.a1', 'projective_image': '960.11358', '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': '12.3'}
  • id: 63520878
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '320.1635', 'aut_weyl_index': 6, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['60.a1.a1', '192.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4882, -1, 6438, -1, 8917, -1, 373, -1], 'generators': [32279025076537209958245527310008417993011626683287199735162127962306528114043151491053460143456309251129114458163026262, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '160.234'}
  • id: 63520879
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '240.i1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 240, 'centralizer': '120.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.h1.a1'], 'contains': ['480.d1.a1', '480.e1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [449, -1, 422, -1, 1282, -1, 8530, -1], 'generators': [66289841429114458251661940245469505153987483175396978279102344394856790155691216444355676337971040928340311792825981386, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872, 49293418623101595405938605219069915167872337233134657159733808100363855209415059371780551046225032982299840478056510918], 'label': '1920.241003.240.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '240.i1.a1', 'projective_image': '1920.241003', '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': '4.2'}
  • id: 63520880
    {'ambient': '1920.241003', 'aut_centralizer_order': 8, 'aut_label': '240.j1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.12', 'aut_weyl_index': 80, 'centralizer': '120.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '120.h1.a1'], 'contains': ['480.e1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [122, -1, 115, -1, 676, -1, 9352, -1], 'generators': [54593569438571673023572183920701744371410899249788967840711683295379597650012246039095251586650046032085321109014207003, 63537184167314187920863286038136291853601699165718856399969194118831573619889462320271337812889349573745390532166441433, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.240.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '240.j1.a1', 'projective_image': '1920.241003', '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': '12.3'}
  • id: 63520881
    {'ambient': '1920.241003', 'aut_centralizer_order': 24, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '80.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.d1.a1', '80.e1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1'], 'contains': ['640.a1.a1', '960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [6146, -1, 5995, -1, 6455, -1, 3632, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 46006712971394263180784344539267020918684943606571499857092863145740169214659963765057870264649117915146808982816516231], 'label': '1920.241003.320.a1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '320.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520882
    {'ambient': '1920.241003', 'aut_centralizer_order': 6, 'aut_label': '320.b1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '160.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.f1.a1', '160.a1.a1'], 'contains': ['640.a1.a1', '960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 160, 'diagramx': [3066, -1, 2641, -1, 3961, -1, 5813, -1], 'generators': [34909022358709995178037630502257206239522394199712338649760120433285611397284361945513872883628022172568553507524006000, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.320.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '160.a1.a1', 'old_label': '320.b1.a1', 'projective_image': '1920.241003', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520883
    {'ambient': '1920.241003', 'aut_centralizer_order': 5, 'aut_label': '384.a1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.1', 'aut_weyl_index': 480, 'centralizer': '192.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6644, -1, 4469, -1, 7335, -1, 2544, -1], 'generators': [32279025076537209958245527310008417993011626683287199735162127962306528114043151491053460143456309251129114458163026262], 'label': '1920.241003.384.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '1920.241003', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520884
    {'ambient': '1920.241003', 'aut_centralizer_order': 192, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.a1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1', '240.d1.a1'], 'contains': ['960.a1.a1', '960.b1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3877, -1, 3408, -1, 4317, -1, 5471, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669], 'label': '1920.241003.480.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520885
    {'ambient': '1920.241003', 'aut_centralizer_order': 96, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.b1.a1', '240.a1.a1', '240.d1.a1', '240.e1.a1', '240.f1.a1', '240.g1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7315, -1, 7806, -1, 6788, -1, 3131, -1], 'generators': [17101720613026535683203701162363171139577591507039102303515362566643115299134217183983702886371253663024542800870928577, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527], 'label': '1920.241003.480.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '480.b1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520886
    {'ambient': '1920.241003', 'aut_centralizer_order': 16, 'aut_label': '480.c1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '120.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.c1.a1', '240.c1.a1', '240.e1.a1', '240.h1.a1'], 'contains': ['960.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 60, 'diagramx': [7935, -1, 4866, -1, 7247, -1, 2651, -1], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 53189539277594972130754827999485283529017066398448821003944801026637096415522484289350368768379552071545917405651447366], 'label': '1920.241003.480.c1.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.b1.a1', 'old_label': '480.c1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520887
    {'ambient': '1920.241003', 'aut_centralizer_order': 32, 'aut_label': '480.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '60.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '240.i1.a1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [1386, -1, 1397, -1, 1939, -1, 7899, -1], 'generators': [66289841429114458251661940245469505153987483175396978279102344394856790155691216444355676337971040928340311792825981386, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.480.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '480.d1.a1', 'projective_image': '1920.241003', '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': '2.1'}
  • id: 63520888
    {'ambient': '1920.241003', 'aut_centralizer_order': 32, 'aut_label': '480.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '60.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1.a1', '240.i1.a1', '240.j1.a1'], 'contains': ['960.b1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [756, -1, 954, -1, 1444, -1, 8375, -1], 'generators': [54593569438571673023572183920701744371410899249788967840711683295379597650012246039095251586650046032085321109014207003, 9852417128305537946413925173538687037555995194593391134244970620239384410492496929841221725100266266001794423872878872], 'label': '1920.241003.480.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.b1.a1', 'old_label': '480.e1.a1', 'projective_image': '1920.241003', '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': '2.1'}
  • id: 63520889
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '384.5602', 'aut_weyl_index': 5, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [3659, -1, 4026, -1, 5604, -1, 4396, -1], 'generators': [66629538133865621729142016747011817950507273664670774591735641163032671328934086437404342602606709905458131814135071452, 17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 59459131085699891964798742515083793186046297286899167588416147733320075934779997173027815067482820764709554668805521399, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669, 3919824752678753122646055768208662651034910100741510554513286076414215184288323089099737874509323718183317834107528775, 18302572616702192083455563329970539974740218082804395813559607590781990311116032505298192063608611322018132096418777137], 'label': '1920.241003.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '960.11358', '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': '192.201'}
  • id: 63520890
    {'ambient': '1920.241003', 'aut_centralizer_order': 24, 'aut_label': '640.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 960, 'centralizer': '80.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.a1.a1', '320.b1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [5630, -1, 4704, -1, 6455, -1, 3632, -1], 'generators': [47761802538344239887648276808250311074344276408092809432557060117819403998279785250374810705629322667777165550858548800], 'label': '1920.241003.640.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '40.d1.a1', 'old_label': '640.a1.a1', 'projective_image': '1920.241003', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '640.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 63520891
    {'ambient': '1920.241003', 'aut_centralizer_order': 1920, 'aut_label': '960.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '320.a1.a1', '480.a1.a1', '480.b1.a1', '480.c1.a1'], 'contains': ['1920.a1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6685, 5000, 5684, 5000, 6788, 5000, 3193, 5000], 'generators': [1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527], 'label': '1920.241003.960.a1.a1', 'mobius_quo': -1, 'mobius_sub': 960, 'normal_closure': '960.a1.a1', 'normal_contained_in': ['60.a1.a1'], 'normal_contains': ['1920.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '960.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': '1.1', 'quotient_action_kernel': '960.11358', 'quotient_action_kernel_order': 960, 'quotient_fusion': None, 'short_label': '960.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520892
    {'ambient': '1920.241003', 'aut_centralizer_order': 192, 'aut_label': '960.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1920, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['320.b1.a1', '480.a1.a1', '480.d1.a1', '480.e1.a1'], 'contains': ['1920.a1.a1'], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3016, -1, 2599, -1, 3961, -1, 5813, -1], 'generators': [317242251954922001468857884084855708500865822808216166161969282647255714279468260521685496206194281742825644863513669], 'label': '1920.241003.960.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '960.b1.a1', 'projective_image': '1920.241003', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520893
    {'ambient': '1920.241003', 'aut_centralizer_order': None, 'aut_label': '1920.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['384.a1.a1', '640.a1.a1', '960.a1.a1', '960.b1.a1'], 'contains': [], 'core': '1920.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5942, 5000, 4555, 5000, 6622, 5000, 3353, 5000], 'generators': [], 'label': '1920.241003.1920.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1920.a1.a1', 'normal_contained_in': ['960.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1920.a1.a1', 'projective_image': '1920.241003', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1920.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 63520894
    {'ambient': '1920.241003', 'aut_centralizer_order': 1, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '120.34', 'aut_weyl_index': 16, 'centralizer': '960.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['80.e1.a1', '96.a1.a1', '160.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [8927, -1, 4555, -1, 9713, -1, 448, -1], 'generators': [15165269849086195961190616024312611043802853554318974853792791318280628132001921388518420123643894082257584878020771885, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 906682211426110278482291418023757106932803422521952317206829887740519517272760662798058216768949828160310084339595040], 'label': '1920.241003.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '960.11358', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 63520895
    {'ambient': '1920.241003', 'aut_centralizer_order': 4, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 40, 'centralizer': '480.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1'], 'contains': ['40.e1.a1', '60.f1.a1', '80.c1.a1'], 'core': '960.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6907, -1, 8680, -1, 7533, -1, 2473, -1], 'generators': [17396283786501090295049723130356813859711847581325208412391716407155784313630064279802334083905743725975646446257646619, 4565305277370936543789577000308551869517291372910520275731418673582902614980390342313327926377221549102832122399233003, 1857197398378889369922854038120556355166913407665381631181585480158175637305296158356581919788296430063076176536218527, 24337102831839339433172965402548596247610569661007581027328916318504031130223955654501767841948526860810182682303761236, 18257266260611490603820436160653704172684775726647994745615646697850086420712988652376309715857887634746681346078771304, 15539738350394393063717573152293571879782704858619538081033238563695012934408484586926715955986719436171711124784800312], 'label': '1920.241003.20.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.a1.a1', 'projective_image': '960.11358', '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': '48.48'}