Abstract group data - 5280.r

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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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 660, 'aut_gen_orders': [20, 10, 12], 'aut_gens': [[44734985446128011, 24133814979398195, 12415902285472309, 6422340100995270, 41772741070013040], [44734985446128011, 13501442332363978, 45822493231479854, 10842363402478390, 41772741070013040], [44734985446128011, 42568814764959284, 36128724638041774, 6422340100995270, 41772741070013040], [6422340100995270, 31837183975835682, 28254458061896337, 5809717384314194, 41772741070013040]], 'aut_group': None, 'aut_hash': 5402696758532746038, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 31680, 'aut_permdeg': 116, 'aut_perms': [1472766104441299305816507186695686492830069762895372869336913247901266981356453061551294454998691458154290289763672656148073600991446578767262053069610686375189605303008560317282282965915399, 6676314203635320993064048394365558297980858493865981886081934449340653024170891281763142445638916548662376851280976856060643371863045719640963122044330905333285598629477133127046, 882615227518360134927206637111469474861849069064443026638903397230903003929000513536810485256798917187394457562936808798515343343179190296269253523215965941636332397365080899455898488697569], 'aut_phi_ratio': 24.75, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 110, 3, 1], [3, 110, 1, 1], [4, 2, 3, 1], [4, 110, 1, 1], [5, 132, 1, 2], [6, 110, 1, 1], [6, 220, 3, 1], [10, 132, 1, 2], [11, 60, 2, 1], [12, 110, 1, 2], [12, 220, 3, 1], [20, 264, 3, 2], [22, 60, 2, 1], [44, 120, 6, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSL(2,11).C_2\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': '7920.q', 'autcentquo_hash': 1157788818429169362, 'autcentquo_nilpotent': False, 'autcentquo_order': 7920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times \\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 110, 3], [3, 110, 1], [4, 2, 3], [4, 110, 1], [5, 132, 2], [6, 110, 1], [6, 220, 3], [10, 132, 2], [11, 60, 2], [12, 110, 2], [12, 220, 3], [20, 264, 6], [22, 60, 2], [44, 120, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '2640.bt', 'commutator_count': 1, 'commutator_label': '1320.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '660.13'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 18, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 110, 1, 3], [3, 110, 1, 1], [4, 2, 1, 3], [4, 110, 1, 1], [5, 132, 2, 1], [6, 110, 1, 1], [6, 220, 1, 3], [10, 132, 2, 1], [11, 60, 2, 1], [12, 110, 2, 1], [12, 220, 1, 3], [20, 264, 2, 3], [22, 60, 2, 1], [44, 120, 2, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 254, 'exponent': 660, 'exponents_of_order': [5, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[12, 0, 2], [20, 1, 3], [24, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2640.bt', 'hash': 4597536282602998348, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [2, 2, 6, 2, 1], 'inner_gens': [[44734985446128011, 24133814979398195, 38125662136079015, 44087814079863762, 41772741070013040], [44734985446128011, 24133814979398195, 41147329439887960, 44087814079863762, 41772741070013040], [5809717384314194, 35215812647737389, 12415902285472309, 6422340100995270, 41772741070013040], [5809717384314194, 26376338987100625, 12415902285472309, 6422340100995270, 41772741070013040], [44734985446128011, 24133814979398195, 12415902285472309, 6422340100995270, 41772741070013040]], 'inner_hash': 6613815745579852445, 'inner_nilpotent': False, 'inner_order': 2640, 'inner_split': True, 'inner_tex': 'C_2^2\\times \\PSL(2,11)', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 4], [5, 8], [10, 8], [11, 4], [12, 10], [20, 3], [24, 2]], 'label': '5280.r', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,11):C2^2', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 39, 'number_divisions': 28, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 69, 'number_subgroup_classes': 170, 'number_subgroups': 11958, 'old_label': None, 'order': 5280, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 331], [3, 110], [4, 116], [5, 264], [6, 770], [10, 264], [11, 120], [12, 880], [20, 1584], [22, 120], [44, 720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [4177274107001304, 23054351874780899], 'outer_gens': [[6422340100995270, 15713267665316284, 42277907939197929, 44734985446128011, 41772741070013040], [6422340100995270, 29435959871950416, 20594434871319655, 10842363402478390, 41772741070013040]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 96, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [10, 12], [11, 4], [20, 1], [24, 5], [40, 1], [48, 1]], 'representations': {'GLFp': {'d': 4, 'p': 11, 'gens': [44734985446128011, 24133814979398195, 12415902285472309, 6422340100995270, 41772741070013040]}, 'Perm': {'d': 96, 'gens': [10339370311181988351046690860219824167752582690464438371460610516989893884451851079408286962005810173694871061406171202140365261579228320182738708506, 21210681968368207302762313911197426671188073837622274806268655254593373239725883492901391202774887809582339316799335757108565342935881437091438997656, 31652816422273714129797368568885609885067582559555568952837277543871407377480362475417030613135682776180642755980871517012221945289905527629481195348, 42092787808822108442840047016235917814623343543992921414296501299834491005069225052426343032016452110422133733185913897629184977717247116571757657628, 52532673456466909767657060937022399580741151165179415121841732413318500496090552229468187461067455319852105342042901017591011927690755172335468241839]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,11):C_2^2', 'transitive_degree': 96, '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: 110571933
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 18, 'group_order': 5280, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 4177274107001304, 'size': 1}
  • id: 110571944
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 18, 'group_order': 5280, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 41772741070013040, 'size': 1}
  • id: 110571955
    {'aut_label': '2B', 'centralizer': '110.f1', 'counter': 3, 'group_counter': 18, 'group_order': 5280, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 11670052188693538, 'size': 110}
  • id: 110571966
    {'aut_label': '2B', 'centralizer': '110.f1', 'counter': 4, 'group_counter': 18, 'group_order': 5280, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 1911328967590449, 'size': 110}
  • id: 110571967
    {'aut_label': '2B', 'centralizer': '110.f1', 'counter': 5, 'group_counter': 18, 'group_order': 5280, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 14740433668903225, 'size': 110}
  • id: 110571968
    {'aut_label': '3A', 'centralizer': '110.a1', 'counter': 6, 'group_counter': 18, 'group_order': 5280, 'label': '3A', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 16693493866733812, 'size': 110}
  • id: 110571969
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 18, 'group_order': 5280, 'label': '4A', 'order': 4, 'powers': [2, 7, 7, 7], 'representative': 5809717384314194, 'size': 2}
  • id: 110571970
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 18, 'group_order': 5280, 'label': '4B', 'order': 4, 'powers': [2, 8, 8, 8], 'representative': 6422340100995270, 'size': 2}
  • id: 110571971
    {'aut_label': '4A', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 18, 'group_order': 5280, 'label': '4C', 'order': 4, 'powers': [2, 9, 9, 9], 'representative': 10842363402478390, 'size': 2}
  • id: 110571934
    {'aut_label': '4D', 'centralizer': '110.a1', 'counter': 10, 'group_counter': 18, 'group_order': 5280, 'label': '4D', 'order': 4, 'powers': [2, 10, 10, 10], 'representative': 44844248644646562, 'size': 110}
  • id: 110571935
    {'aut_label': '5A1', 'centralizer': '132.c1', 'counter': 11, 'group_counter': 18, 'group_order': 5280, 'label': '5A1', 'order': 5, 'powers': [12, 12, 1, 11], 'representative': 10388781187412640, 'size': 132}
  • id: 110571936
    {'aut_label': '5A2', 'centralizer': '132.c1', 'counter': 12, 'group_counter': 18, 'group_order': 5280, 'label': '5A2', 'order': 5, 'powers': [11, 11, 1, 12], 'representative': 22743034787395584, 'size': 132}
  • id: 110571937
    {'aut_label': '6A', 'centralizer': '110.a1', 'counter': 13, 'group_counter': 18, 'group_order': 5280, 'label': '6A', 'order': 6, 'powers': [6, 2, 13, 13], 'representative': 20870767973735116, 'size': 110}
  • id: 110571938
    {'aut_label': '6B', 'centralizer': '220.a1', 'counter': 14, 'group_counter': 18, 'group_order': 5280, 'label': '6B', 'order': 6, 'powers': [6, 3, 14, 14], 'representative': 11593645036204447, 'size': 220}
  • id: 110571939
    {'aut_label': '6B', 'centralizer': '220.a1', 'counter': 15, 'group_counter': 18, 'group_order': 5280, 'label': '6C', 'order': 6, 'powers': [6, 4, 15, 15], 'representative': 15497041408893894, 'size': 220}
  • id: 110571940
    {'aut_label': '6B', 'centralizer': '220.a1', 'counter': 16, 'group_counter': 18, 'group_order': 5280, 'label': '6D', 'order': 6, 'powers': [6, 5, 16, 16], 'representative': 45694331319549695, 'size': 220}
  • id: 110571941
    {'aut_label': '10A1', 'centralizer': '132.c1', 'counter': 17, 'group_counter': 18, 'group_order': 5280, 'label': '10A1', 'order': 10, 'powers': [11, 18, 2, 17], 'representative': 39451845901958628, 'size': 132}
  • id: 110571942
    {'aut_label': '10A3', 'centralizer': '132.c1', 'counter': 18, 'group_counter': 18, 'group_order': 5280, 'label': '10A3', 'order': 10, 'powers': [12, 17, 2, 18], 'representative': 43806974041651511, 'size': 132}
  • id: 110571943
    {'aut_label': '11A1', 'centralizer': '60.a1', 'counter': 19, 'group_counter': 18, 'group_order': 5280, 'label': '11A1', 'order': 11, 'powers': [20, 19, 19, 1], 'representative': 7712880704158785, 'size': 60}
  • id: 110571945
    {'aut_label': '11A1', 'centralizer': '60.a1', 'counter': 20, 'group_counter': 18, 'group_order': 5280, 'label': '11A-1', 'order': 11, 'powers': [19, 20, 20, 1], 'representative': 5236355182758855, 'size': 60}
  • id: 110571946
    {'aut_label': '12A1', 'centralizer': '110.a1', 'counter': 21, 'group_counter': 18, 'group_order': 5280, 'label': '12A1', 'order': 12, 'powers': [13, 10, 22, 21], 'representative': 34954089406423196, 'size': 110}
  • id: 110571947
    {'aut_label': '12A5', 'centralizer': '110.a1', 'counter': 22, 'group_counter': 18, 'group_order': 5280, 'label': '12A5', 'order': 12, 'powers': [13, 10, 21, 22], 'representative': 9890444764415372, 'size': 110}
  • id: 110571948
    {'aut_label': '12B', 'centralizer': '220.a1', 'counter': 23, 'group_counter': 18, 'group_order': 5280, 'label': '12B', 'order': 12, 'powers': [13, 9, 23, 23], 'representative': 29032989919486175, 'size': 220}
  • id: 110571949
    {'aut_label': '12B', 'centralizer': '220.a1', 'counter': 24, 'group_counter': 18, 'group_order': 5280, 'label': '12C', 'order': 12, 'powers': [13, 8, 24, 24], 'representative': 32062081290131137, 'size': 220}
  • id: 110571950
    {'aut_label': '12B', 'centralizer': '220.a1', 'counter': 25, 'group_counter': 18, 'group_order': 5280, 'label': '12D', 'order': 12, 'powers': [13, 7, 25, 25], 'representative': 17552469581752946, 'size': 220}
  • id: 110571951
    {'aut_label': '20A1', 'centralizer': '264.b1', 'counter': 26, 'group_counter': 18, 'group_order': 5280, 'label': '20A1', 'order': 20, 'powers': [17, 27, 7, 26], 'representative': 2485379310770243, 'size': 264}
  • id: 110571952
    {'aut_label': '20A3', 'centralizer': '264.b1', 'counter': 27, 'group_counter': 18, 'group_order': 5280, 'label': '20A3', 'order': 20, 'powers': [18, 26, 7, 27], 'representative': 15657685156207599, 'size': 264}
  • id: 110571953
    {'aut_label': '20A3', 'centralizer': '264.b1', 'counter': 28, 'group_counter': 18, 'group_order': 5280, 'label': '20B1', 'order': 20, 'powers': [18, 29, 9, 28], 'representative': 25672954312212710, 'size': 264}
  • id: 110571954
    {'aut_label': '20A1', 'centralizer': '264.b1', 'counter': 29, 'group_counter': 18, 'group_order': 5280, 'label': '20B3', 'order': 20, 'powers': [17, 28, 9, 29], 'representative': 6335740077364691, 'size': 264}
  • id: 110571956
    {'aut_label': '20A1', 'centralizer': '264.b1', 'counter': 30, 'group_counter': 18, 'group_order': 5280, 'label': '20C1', 'order': 20, 'powers': [17, 31, 8, 30], 'representative': 42063278138147798, 'size': 264}
  • id: 110571957
    {'aut_label': '20A3', 'centralizer': '264.b1', 'counter': 31, 'group_counter': 18, 'group_order': 5280, 'label': '20C3', 'order': 20, 'powers': [18, 30, 8, 31], 'representative': 1869735297268513, 'size': 264}
  • id: 110571958
    {'aut_label': '22A1', 'centralizer': '60.a1', 'counter': 32, 'group_counter': 18, 'group_order': 5280, 'label': '22A1', 'order': 22, 'powers': [19, 32, 32, 2], 'representative': 42321125146952288, 'size': 60}
  • id: 110571959
    {'aut_label': '22A1', 'centralizer': '60.a1', 'counter': 33, 'group_counter': 18, 'group_order': 5280, 'label': '22A-1', 'order': 22, 'powers': [20, 33, 33, 2], 'representative': 45819044665988824, 'size': 60}
  • id: 110571960
    {'aut_label': '44A1', 'centralizer': '120.a1', 'counter': 34, 'group_counter': 18, 'group_order': 5280, 'label': '44A1', 'order': 44, 'powers': [32, 34, 34, 8], 'representative': 31775989510637638, 'size': 120}
  • id: 110571961
    {'aut_label': '44A1', 'centralizer': '120.a1', 'counter': 35, 'group_counter': 18, 'group_order': 5280, 'label': '44A-1', 'order': 44, 'powers': [33, 35, 35, 8], 'representative': 39680212606263596, 'size': 120}
  • id: 110571962
    {'aut_label': '44A1', 'centralizer': '120.a1', 'counter': 36, 'group_counter': 18, 'group_order': 5280, 'label': '44B1', 'order': 44, 'powers': [33, 36, 36, 9], 'representative': 28695260657549509, 'size': 120}
  • id: 110571963
    {'aut_label': '44A1', 'centralizer': '120.a1', 'counter': 37, 'group_counter': 18, 'group_order': 5280, 'label': '44B-1', 'order': 44, 'powers': [32, 37, 37, 9], 'representative': 45819563145219429, 'size': 120}
  • id: 110571964
    {'aut_label': '44A1', 'centralizer': '120.a1', 'counter': 38, 'group_counter': 18, 'group_order': 5280, 'label': '44C1', 'order': 44, 'powers': [33, 38, 38, 7], 'representative': 23052284295703120, 'size': 120}
  • id: 110571965
    {'aut_label': '44A1', 'centralizer': '120.a1', 'counter': 39, 'group_counter': 18, 'group_order': 5280, 'label': '44C-1', 'order': 44, 'powers': [32, 39, 39, 7], 'representative': 30079599215939003, 'size': 120}
• 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: 4667672
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4667683
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4667693
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4667694
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4667695
    {'cdim': 5, 'counter': 5, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.5a', 'multiplicity': 2, 'nt': [55, 0], 'qdim': 10, 'qvalues': [10, 10, 2, 2, 2, -2, 10, 10, 10, 2, 0, 0, -2, 2, 2, 2, 0, 0, -1, -1, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4667696
    {'cdim': 5, 'counter': 6, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.5b', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, 10, -2, -2, 2, -2, 10, -10, -10, 2, 0, 0, -2, -2, 2, -2, 0, 0, -1, -1, 2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4667697
    {'cdim': 5, 'counter': 7, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.5c', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, 10, -2, 2, -2, -2, -10, -10, 10, 2, 0, 0, -2, 2, -2, -2, 0, 0, -1, -1, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4667698
    {'cdim': 5, 'counter': 8, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.5d', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, 10, 2, -2, -2, -2, -10, 10, -10, 2, 0, 0, -2, -2, -2, 2, 0, 0, -1, -1, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4667699
    {'cdim': 10, 'counter': 9, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10a', 'multiplicity': 1, 'nt': [11, 5], 'qdim': 10, 'qvalues': [10, 10, 2, 2, 2, 1, 10, 10, 10, 2, 0, 0, 1, -1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4667673
    {'cdim': 10, 'counter': 10, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10b', 'multiplicity': 1, 'nt': [22, 13], 'qdim': 10, 'qvalues': [10, 10, -2, -2, 2, 1, 10, -10, -10, 2, 0, 0, 1, 1, -1, 1, 0, 0, -1, -1, -1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4667674
    {'cdim': 10, 'counter': 11, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10c', 'multiplicity': 1, 'nt': [22, 13], 'qdim': 10, 'qvalues': [10, 10, -2, 2, -2, 1, -10, -10, 10, 2, 0, 0, 1, -1, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4667675
    {'cdim': 10, 'counter': 12, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10d', 'multiplicity': 1, 'nt': [22, 13], 'qdim': 10, 'qvalues': [10, 10, 2, -2, -2, 1, -10, 10, -10, 2, 0, 0, 1, 1, 1, -1, 0, 0, -1, -1, -1, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4667676
    {'cdim': 10, 'counter': 13, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10e', 'multiplicity': 1, 'nt': [55, 0], 'qdim': 10, 'qvalues': [10, 10, -2, -2, -2, 1, 10, 10, 10, -2, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4667677
    {'cdim': 10, 'counter': 14, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10f', 'multiplicity': 1, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, 10, -2, 2, 2, 1, -10, 10, -10, -2, 0, 0, 1, -1, -1, 1, 0, 0, -1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 4667678
    {'cdim': 10, 'counter': 15, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10g', 'multiplicity': 1, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, 10, 2, -2, 2, 1, -10, -10, 10, -2, 0, 0, 1, 1, -1, -1, 0, 0, -1, -1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4667679
    {'cdim': 10, 'counter': 16, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.10h', 'multiplicity': 1, 'nt': [110, 0], 'qdim': 10, 'qvalues': [10, 10, 2, 2, -2, 1, 10, -10, -10, -2, 0, 0, 1, -1, 1, -1, 0, 0, -1, -1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 4667680
    {'cdim': 11, 'counter': 17, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.11a', 'multiplicity': 1, 'nt': [12, 179], 'qdim': 11, 'qvalues': [11, 11, -1, -1, -1, -1, 11, 11, 11, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667681
    {'cdim': 11, 'counter': 18, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.11b', 'multiplicity': 1, 'nt': [24, 2948], 'qdim': 11, 'qvalues': [11, 11, -1, 1, 1, -1, -11, 11, -11, -1, 1, 1, -1, 1, 1, -1, 1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667682
    {'cdim': 11, 'counter': 19, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.11c', 'multiplicity': 1, 'nt': [24, 2948], 'qdim': 11, 'qvalues': [11, 11, 1, -1, 1, -1, -11, -11, 11, -1, 1, 1, -1, -1, 1, 1, 1, 1, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667684
    {'cdim': 11, 'counter': 20, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.11d', 'multiplicity': 1, 'nt': [24, 2948], 'qdim': 11, 'qvalues': [11, 11, 1, 1, -1, -1, 11, -11, -11, -1, 1, 1, -1, 1, -1, 1, 1, 1, 0, 0, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667690
    {'cdim': 20, 'counter': 26, 'faithful': True, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.20a', 'multiplicity': 1, 'nt': [440, 0], 'qdim': 20, 'qvalues': [20, -20, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667685
    {'cdim': 12, 'counter': 21, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.12a', 'multiplicity': 2, 'nt': [55, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, 24, 24, 24, 0, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 4667686
    {'cdim': 12, 'counter': 22, 'faithful': True, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.12b', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667687
    {'cdim': 12, 'counter': 23, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.12c', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, -24, -24, 24, 0, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, 2, 2, 2, 2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 4667688
    {'cdim': 12, 'counter': 24, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.12d', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, -24, 24, -24, 0, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 2, 2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 4667689
    {'cdim': 12, 'counter': 25, 'faithful': False, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.12e', 'multiplicity': 2, 'nt': [110, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, 0, 0, 24, -24, -24, 0, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 2, 2, -2, -2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 4667691
    {'cdim': 20, 'counter': 27, 'faithful': True, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.20b', 'multiplicity': 2, 'nt': [440, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4667692
    {'cdim': 24, 'counter': 28, 'faithful': True, 'group': '5280.r', 'group_order': 5280, 'image': None, 'label': '5280.r.24a', 'multiplicity': 2, 'nt': [440, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 7479392
    {'center': '1.a1', 'center_index': 1, 'center_order': 5280, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 5280, 'label': '5280.r.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479403
    {'center': '1.a1', 'center_index': 1, 'center_order': 5280, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 2640, 'label': '5280.r.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479414
    {'center': '1.a1', 'center_index': 1, 'center_order': 5280, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 2640, 'label': '5280.r.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479425
    {'center': '1.a1', 'center_index': 1, 'center_order': 5280, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 2640, 'label': '5280.r.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479426
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 5, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 0, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.5a1', 'nt': [55, 0], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7479427
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 6, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 0, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.5a2', 'nt': [55, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7479428
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 7, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.5b1', 'nt': [110, 0], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7479429
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 8, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.5b2', 'nt': [110, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7479430
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 9, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.5c1', 'nt': [110, 0], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7479393
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 10, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.5c2', 'nt': [110, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7479394
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 11, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.5d1', 'nt': [110, 0], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]]]}
  • id: 7479395
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 12, 'cyclotomic_n': 11, 'dim': 5, 'faithful': False, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 0, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.5d2', 'nt': [110, 2], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 0], [1, 1], [1, 3], [1, 4], [1, 5], [1, -2]], [[-1, 0], [-1, 1], [-1, 3], [-1, 4], [-1, 5], [-1, -2]], [[1, 1], [1, 3], [1, 4], [1, 5], [1, -2]]]}
  • id: 7479396
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 13, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.10a', 'nt': [11, 5], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479397
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 14, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.10b', 'nt': [22, 13], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[10, 0]], [[-10, 0]], [[-10, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479398
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 15, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.10c', 'nt': [22, 13], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-10, 0]], [[-10, 0]], [[10, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479399
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 16, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.10d', 'nt': [22, 13], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-10, 0]], [[10, 0]], [[-10, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479400
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.10e', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[10, 0]], [[10, 0]], [[10, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479401
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.10f', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-10, 0]], [[10, 0]], [[-10, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479402
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.10g', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-10, 0]], [[-10, 0]], [[10, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479404
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.10h', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[10, 0]], [[-10, 0]], [[-10, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479405
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 1, 'dim': 11, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.11a', 'nt': [12, 179], 'q_character': None, 'values': [[[11, 0]], [[11, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[11, 0]], [[11, 0]], [[11, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479406
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 1, 'dim': 11, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.11b', 'nt': [24, 2948], 'q_character': None, 'values': [[[11, 0]], [[11, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-11, 0]], [[11, 0]], [[-11, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479407
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 23, 'cyclotomic_n': 1, 'dim': 11, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.11c', 'nt': [24, 2948], 'q_character': None, 'values': [[[11, 0]], [[11, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-11, 0]], [[-11, 0]], [[11, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479408
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 24, 'cyclotomic_n': 1, 'dim': 11, 'faithful': False, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.11d', 'nt': [24, 2948], 'q_character': None, 'values': [[[11, 0]], [[11, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[11, 0]], [[-11, 0]], [[-11, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479409
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 25, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.12a1', 'nt': [55, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479410
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 26, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '660.13', 'image_order': 660, 'indicator': 1, 'kernel': '660.a1', 'kernel_order': 8, 'label': '5280.r.12a2', 'nt': [55, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479411
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 11, 'dim': 12, 'faithful': True, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 0, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.12b1', 'nt': [96, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479412
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 11, 'dim': 12, 'faithful': True, 'field': [3, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 0, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.12b2', 'nt': [96, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0], [2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479413
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.12c1', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479415
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.12c2', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479416
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.12d1', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[12, 0]], [[-12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479417
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.12d2', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[12, 0]], [[-12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7479418
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.12e1', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[-12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479419
    {'center': '660.a1', 'center_index': 660, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 5, 'dim': 12, 'faithful': False, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '1320.134', 'image_order': 1320, 'indicator': 1, 'kernel': '1320.a1', 'kernel_order': 4, 'label': '5280.r.12e2', 'nt': [110, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-12, 0]], [[-12, 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]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7479420
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 1, 'dim': 20, 'faithful': True, 'field': [0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 1, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.20a', 'nt': [440, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479421
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 36, 'cyclotomic_n': 12, 'dim': 20, 'faithful': True, 'field': [-3, 0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 1, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.20b1', 'nt': [440, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479422
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 37, 'cyclotomic_n': 12, 'dim': 20, 'faithful': True, 'field': [-3, 0, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 1, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.20b2', 'nt': [440, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479423
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 38, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 1, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.24a1', 'nt': [440, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7479424
    {'center': '2640.a1', 'center_index': 2640, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 5, 'dim': 24, 'faithful': True, 'field': [-1, -1, 1], 'group': '5280.r', 'group_counter': 18, 'group_order': 5280, 'image': None, 'image_isoclass': '5280.r', 'image_order': 5280, 'indicator': 1, 'kernel': '5280.a1', 'kernel_order': 1, 'label': '5280.r.24a2', 'nt': [440, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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: 67423697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 5280, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 330, 'label': '5280.r.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5280.r', 'subgroup_hash': 4597536282602998348, 'subgroup_order': 5280, 'subgroup_tex': '\\SL(2,11):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67423708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2640, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5280.r.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2640.l', 'subgroup_hash': 6650082401052208970, 'subgroup_order': 2640, 'subgroup_tex': '\\SL(2,11):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67423719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1320, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5280.r.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': ['D', 'PC', 'L1', 'D1', 'D', 'PC', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1320.13', 'subgroup_hash': 13, 'subgroup_order': 1320, 'subgroup_tex': '\\SL(2,11)', 'supersolvable': False, 'sylow': 0}
  • id: 67423730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '5280.r.11.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.959', 'subgroup_hash': 959, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,5):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67423741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.12.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, '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': '440.14', 'subgroup_hash': 14, 'subgroup_order': 440, 'subgroup_tex': 'C_{44}.C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 67423752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.22.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.93', 'subgroup_hash': 93, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
  • id: 67423763
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '220.2', 'subgroup_hash': 2, 'subgroup_order': 220, 'subgroup_tex': 'C_{11}:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 67423764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.44.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.a1', 'outer_equivalence': True, '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': 44, '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: 67423765
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 67423698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '5280.r.55.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.201', 'subgroup_hash': 201, 'subgroup_order': 96, 'subgroup_tex': '\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 67423699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '5280.r.55.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.216', 'subgroup_hash': 216, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 67423700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 8, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.60.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.a1', 'outer_equivalence': True, 'perfect': False, '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': '88.10', 'subgroup_hash': 10, 'subgroup_order': 88, 'subgroup_tex': 'Q_8\\times C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 67423701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.66.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '66.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.42', 'subgroup_hash': 42, 'subgroup_order': 80, 'subgroup_tex': 'D_{20}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67423702
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 55, 'label': '5280.r.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, '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': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 67423703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.110.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 67423704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.110.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': 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: 67423705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.110.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67423706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.110.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.41', 'subgroup_hash': 41, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 67423707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.110.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67423709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.110.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67423710
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 4, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.120.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.a1', 'outer_equivalence': True, 'perfect': False, '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': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
  • id: 67423711
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.132.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 67423712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.132.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 67423713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.132.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67423714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '5280.r.165.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '165.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 165, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 67423715
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67423716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': 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: 67423717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 67423718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67423720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67423721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 67423722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 67423723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67423724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': 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: 67423725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.220.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, 'quotient_simple': 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: 67423726
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.240.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.a1', 'outer_equivalence': True, 'perfect': False, '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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 67423727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.264.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 67423728
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.264.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 67423729
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.264.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67423731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.330.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 330, 'quotient_simple': 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: 67423732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.330.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 330, 'quotient_simple': 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: 67423733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.330.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '330.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 330, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 67423734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.440.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': 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: 67423735
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.440.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 67423736
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.440.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': 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: 67423737
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.440.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': 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: 67423738
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.440.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': 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: 67423739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.440.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 67423740
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 88, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 11, 'label': '5280.r.480.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '480.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 67423742
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.528.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 67423743
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.528.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '528.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 67423744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 1320, 'characteristic': True, 'core_order': 8, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5280.r.660.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '660.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '660.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 660, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,11)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'C1', 'F', 'R', 'U0', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 67423745
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.660.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, 'quotient_simple': 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: 67423746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.660.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, 'quotient_simple': 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: 67423747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.660.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, 'quotient_simple': 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: 67423748
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.660.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 67423749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.660.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '660.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 660, 'quotient_simple': 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: 67423750
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.880.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '880.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 880, 'quotient_simple': 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: 67423751
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.880.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '880.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 880, 'quotient_simple': 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: 67423753
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.880.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '880.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 67423754
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '5280.r.1056.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1056.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1056, '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: 67423755
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 2640, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5280.r.1320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1320.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1320.134', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 134, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1320, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\PSL(2,11)', 'simple': False, 'solvable': True, 'special_labels': ['C2', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67423756
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.1320.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1320, 'quotient_simple': 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: 67423757
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.1320.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1320, 'quotient_simple': 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: 67423758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5280.r.1320.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1320, 'quotient_simple': 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: 67423759
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '5280.r.1760.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1760.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1760, '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: 67423760
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 5280, 'characteristic': True, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5280.r.2640.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2640.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2640.bt', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6613815745579852445, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2640, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times \\PSL(2,11)', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'S', 'U1', 'C3', 'Z', 'Phi', 'S', 'U1', 'C3'], '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: 67423761
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5280.r.2640.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2640.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2640, '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: 67423762
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5280.r', 'ambient_counter': 18, 'ambient_order': 5280, 'ambient_tex': '\\SL(2,11):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 5280, 'characteristic': True, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '5280.r.5280.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5280.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '5280.r', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4597536282602998348, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 5280, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,11):C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'C4', 'U2', 'C4'], '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: 67423738
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '440.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['44.a1', '220.c1', '220.d1', '220.i1'], 'contains': ['880.a1', '1320.c1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [3691, -1, 6236, -1], 'generators': [20593714479174394, 19369420327978728, 41772741070013040], 'label': '5280.r.440.e1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '440.e1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 67423739
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '440.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['220.g1'], 'contains': ['880.b1', '880.c1', '1320.d1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 1320, 'diagramx': [9577, -1, 8532, -1], 'generators': [31622909906065936, 44067934411623013, 33405471707136862], 'label': '5280.r.440.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '220.g1', 'old_label': '440.f1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 67423740
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '240.a1'], 'contains': ['5280.a1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1061, -1, 2210, -1], 'generators': [19082840468861376], 'label': '5280.r.480.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '480.a1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
  • id: 67423741
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['24.a1', '60.a1', '132.c1'], 'core': '660.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1458, -1, 1778, -1], 'generators': [44734985446128011, 32826061769933604, 13475989786637005, 6422340100995270, 41772741070013040], 'label': '5280.r.12.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '12.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '220.8'}
  • id: 67423742
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '528.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '132.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '264.a1', '264.b1', '264.c1'], 'contains': ['1056.a1', '2640.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1893, -1, 2779, -1], 'generators': [17575135970880675, 41772741070013040], 'label': '5280.r.528.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '528.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423743
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '528.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['264.a1'], 'contains': ['1056.a1', '2640.b1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 396, 'diagramx': [2457, -1, 3125, -1], 'generators': [41775075631649601, 32935044166904759], 'label': '5280.r.528.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '132.a1', 'old_label': '528.b1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 67423730
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['22.a1', '55.a1', '66.a1', '110.d1'], 'core': '660.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4139, -1, 3936, -1], 'generators': [44734985446128011, 39668646791340708, 20769037021042451, 6422340100995270, 41772741070013040], 'label': '5280.r.11.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1', 'old_label': '11.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1', 'subgroup_fusion': None, 'weyl_group': '240.190'}
  • id: 67423731
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '330.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['110.b1', '110.c1', '165.a1'], 'contains': ['660.b1', '660.d1', '660.f1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [4632, -1, 5132, -1], 'generators': [12052125667637317, 39102834447932290, 6422340100995270, 41772741070013040], 'label': '5280.r.330.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1', 'old_label': '330.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67423732
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '330.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '440.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['66.a1', '110.a1', '110.d1', '165.a1'], 'contains': ['660.a1', '660.b1', '660.c1'], 'core': '660.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5658, -1, 4570, -1], 'generators': [44734985446128011, 39102834447932290, 6422340100995270, 41772741070013040], 'label': '5280.r.330.b1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '330.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67423733
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '330.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['110.e1', '110.f1', '165.a1'], 'contains': ['660.b1', '660.c1', '660.d1', '660.e1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 495, 'diagramx': [9095, -1, 8287, -1], 'generators': [12052125667637317, 5455705447089206, 6422340100995270, 41772741070013040], 'label': '5280.r.330.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1', 'old_label': '330.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '330.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67423734
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '220.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['220.a1', '220.b1', '220.d1', '220.g1'], 'contains': ['880.a1', '880.b1', '1320.b1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8211, -1, 7730, -1], 'generators': [24042258004896203, 17136092714415672, 41772741070013040], 'label': '5280.r.440.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '440.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423735
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['220.c1', '220.d1', '220.e1', '220.f1', '220.g1'], 'contains': ['880.a1', '880.c1', '1320.b1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [7582, -1, 7281, -1], 'generators': [20593714479174394, 13556750675449154, 41772741070013040], 'label': '5280.r.440.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '440.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 67423736
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '220.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['110.b1', '220.a1', '220.b1', '220.c1', '220.e1', '220.h1'], 'contains': ['880.a1', '1320.a1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [6383, -1, 5537, -1], 'generators': [6422340100995270, 45374894364654351, 41772741070013040], 'label': '5280.r.440.c1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '440.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423737
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '440.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.a1', '220.f1', '220.i1'], 'contains': ['880.a1', '1320.c1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5897, -1, 6625, -1], 'generators': [14204662257555855, 17136092714415672, 41772741070013040], 'label': '5280.r.440.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '440.d1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423697
    {'ambient': '5280.r', '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': '2640.a1', 'complements': ['5280.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '11.a1', '12.a1', '55.b1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3914, 3458, 3638, 3487], 'generators': [44734985446128011, 24133814979398195, 6422340100995270, 14280958855506462, 41772741070013040], 'label': '5280.r.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '660.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '2640.bt'}
  • id: 67423698
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1'], 'contains': ['110.b1', '165.a1', '220.h1'], 'core': '660.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5060, -1, 4204, -1], 'generators': [44734985446128011, 12052125667637317, 39102834447932290, 6422340100995270, 45374894364654351, 41772741070013040], 'label': '5280.r.55.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1', 'old_label': '55.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 67423699
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['110.a1', '110.c1', '110.d1', '110.e1', '110.f1', '165.a1'], 'core': '660.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6140, -1, 5831, -1], 'generators': [44734985446128011, 24133814979398195, 17136092714415672, 6422340100995270, 6047697104471813, 41772741070013040], 'label': '5280.r.55.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '55.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 67423700
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '240.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1'], 'contains': ['120.a1', '660.a1'], 'core': '660.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [281, -1, 1152, -1], 'generators': [44734985446128011, 13475989786637005, 6422340100995270, 41772741070013040], 'label': '5280.r.60.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '60.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1', 'subgroup_fusion': None, 'weyl_group': '20.5'}
  • id: 67423701
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '66.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1'], 'contains': ['132.a1', '132.b1', '132.c1', '330.b1'], 'core': '660.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2808, -1, 2538, -1], 'generators': [44735138646218703, 44734985446128011, 17575135970880675, 6422340100995270, 41772741070013040], 'label': '5280.r.66.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '66.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.a1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 67423702
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1'], 'contains': ['480.a1', '1056.a1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1269, -1, 1761, -1], 'generators': [12226499370669534, 19082840468861376], 'label': '5280.r.96.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '96.a1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}
  • id: 67423703
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '110.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '440.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1'], 'contains': ['220.a1', '220.b1', '220.h1', '330.b1'], 'core': '660.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [6680, -1, 5226, -1], 'generators': [44734985446128011, 17136092714415672, 6422340100995270, 6047697104471813, 41772741070013040], 'label': '5280.r.110.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '110.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67423704
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['22.a1', '55.a1'], 'contains': ['220.j1', '330.a1', '440.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [4752, -1, 3630, -1], 'generators': [12052125667637317, 39102834447932290, 6422340100995270, 45374894364654351, 41772741070013040], 'label': '5280.r.110.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1', 'old_label': '110.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 67423705
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '55.b1'], 'contains': ['220.a1', '220.c1', '220.d1', '220.f1', '220.i1', '330.a1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [5357, -1, 6331, -1], 'generators': [29885696370473409, 17136092714415672, 6047697104471813, 10842363402478390, 41772741070013040], 'label': '5280.r.110.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '110.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 67423706
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['11.a1', '55.b1'], 'contains': ['220.c1', '220.e1', '220.h1', '330.b1'], 'core': '660.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [6140, -1, 4622, -1], 'generators': [44734985446128011, 41108587751539980, 3867401663483908, 6422340100995270, 41772741070013040], 'label': '5280.r.110.d1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '110.d1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 67423707
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['55.b1'], 'contains': ['220.b1', '220.c1', '220.d1', '220.e1', '220.g1', '330.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [8184, -1, 7639, -1], 'generators': [24133814979398195, 24042258004896203, 17136092714415672, 10842363402478390, 41772741070013040], 'label': '5280.r.110.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '110.e1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
  • id: 67423708
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': ['2640.b1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '22.a1', '24.a1', '110.c1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3699, 3458, 3340, 3487], 'generators': [3728074135169800, 29885696370473409, 10842363402478390, 41772741070013040], 'label': '5280.r.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '1320.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '2640.bt', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '1320.134'}
  • id: 67423709
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '110.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['55.b1'], 'contains': ['220.a1', '220.e1', '220.f1', '220.g1', '330.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7606, -1, 8287, -1], 'generators': [24133814979398195, 24042258004896203, 17136092714415672, 6422340100995270, 41772741070013040], 'label': '5280.r.110.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '110.f1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 67423710
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '60.a1'], 'contains': ['240.a1', '1320.a1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [551, -1, 2016, -1], 'generators': [6422340100995270, 19082840468861376, 41772741070013040], 'label': '5280.r.120.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '120.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 67423711
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['22.a1', '66.a1'], 'contains': ['264.a1', '264.b1', '264.c1', '660.b1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [2958, -1, 2779, -1], 'generators': [44735138646218703, 44734985446128011, 17575135970880675, 41772741070013040], 'label': '5280.r.132.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '132.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 67423712
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '132.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['66.a1'], 'contains': ['264.a1', '264.b1', '660.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [2523, -1, 2292, -1], 'generators': [41775075631649601, 17575135970880675, 6422340100995270, 41772741070013040], 'label': '5280.r.132.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '132.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.b1', 'subgroup_fusion': None, 'weyl_group': '40.13'}
  • id: 67423713
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '132.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '528.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '66.a1'], 'contains': ['264.b1', '660.a1'], 'core': '660.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1937, -1, 1804, -1], 'generators': [44734985446128011, 17575135970880675, 6422340100995270, 41772741070013040], 'label': '5280.r.132.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '132.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67423714
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '165.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2640.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1', '55.b1'], 'contains': ['330.a1', '330.b1', '330.c1'], 'core': '660.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5700, -1, 5831, -1], 'generators': [44734985446128011, 12052125667637317, 39102834447932290, 6422340100995270, 41772741070013040], 'label': '5280.r.165.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1', 'old_label': '165.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 67423715
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '220.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['110.a1', '110.c1', '110.f1'], 'contains': ['440.a1', '440.c1', '440.d1', '660.b1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7471, -1, 6664, -1], 'generators': [31622909906065936, 44734985446128011, 17136092714415672, 41772741070013040], 'label': '5280.r.220.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423716
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '440.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['110.a1', '110.e1'], 'contains': ['440.a1', '440.c1', '660.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [8392, -1, 7695, -1], 'generators': [17136092714415672, 6422340100995270, 6047697104471813, 41772741070013040], 'label': '5280.r.220.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67423717
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['22.a1', '110.c1', '110.d1', '110.e1'], 'contains': ['440.b1', '440.c1', '440.e1', '660.b1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [4864, -1, 6021, -1], 'generators': [20593714479174394, 44734985446128011, 3867401663483908, 41772741070013040], 'label': '5280.r.220.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 67423718
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['110.c1', '110.e1'], 'contains': ['440.a1', '440.b1', '440.e1', '660.d1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [6977, -1, 9167, -1], 'generators': [31622909906065936, 24133814979398195, 17136092714415672, 41772741070013040], 'label': '5280.r.220.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.d1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 67423719
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': ['1320.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['44.a1', '48.a1', '220.i1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3193, 3458, 2913, 3487], 'generators': [30060383679096532, 29885696370473409, 41772741070013040], 'label': '5280.r.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['2640.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '2640.bt', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '660.13'}
  • id: 67423720
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['110.d1', '110.e1', '110.f1'], 'contains': ['440.b1', '440.c1', '660.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [7956, -1, 7207, -1], 'generators': [41108587751539980, 3867401663483908, 6422340100995270, 41772741070013040], 'label': '5280.r.220.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.e1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 67423721
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['110.c1', '110.f1'], 'contains': ['440.b1', '440.d1', '660.d1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [6626, -1, 8774, -1], 'generators': [44067934411623013, 14204662257555855, 17136092714415672, 41772741070013040], 'label': '5280.r.220.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.f1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 67423722
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['110.e1', '110.f1'], 'contains': ['440.a1', '440.b1', '440.f1', '660.e1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [9299, -1, 9702, -1], 'generators': [31622909906065936, 34831149871170920, 17136092714415672, 41772741070013040], 'label': '5280.r.220.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.g1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 67423723
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '440.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1', '110.a1', '110.d1'], 'contains': ['440.c1', '660.a1'], 'core': '660.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5893, -1, 4074, -1], 'generators': [44734985446128011, 6422340100995270, 45374894364654351, 41772741070013040], 'label': '5280.r.220.h1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.h1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 67423724
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '110.c1'], 'contains': ['440.d1', '440.e1', '660.f1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [3398, -1, 5529, -1], 'generators': [14204662257555855, 29885696370473409, 17136092714415672, 41772741070013040], 'label': '5280.r.220.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '220.i1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 67423725
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '220.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1', '110.b1'], 'contains': ['660.f1', '880.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [3969, -1, 3427, -1], 'generators': [12052125667637317, 39102834447932290, 4744352207913140, 41772741070013040], 'label': '5280.r.220.j1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1', 'old_label': '220.j1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.j1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67423726
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '120.a1'], 'contains': ['480.a1', '2640.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [767, -1, 2210, -1], 'generators': [19082840468861376, 41772741070013040], 'label': '5280.r.240.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '240.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
  • id: 67423727
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '264.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['132.a1', '132.b1'], 'contains': ['528.a1', '528.b1', '1320.b1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [2669, -1, 2779, -1], 'generators': [41775075631649601, 17575135970880675, 41772741070013040], 'label': '5280.r.264.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '264.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
  • id: 67423728
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '264.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '264.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '132.a1', '132.b1', '132.c1'], 'contains': ['528.a1', '1320.a1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 198, 'diagramx': [1824, -1, 2395, -1], 'generators': [17575135970880675, 6422340100995270, 41772741070013040], 'label': '5280.r.264.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '264.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423729
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1', '132.a1'], 'contains': ['528.a1', '1320.c1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [2171, -1, 3172, -1], 'generators': [44735138646218703, 17575135970880675, 41772741070013040], 'label': '5280.r.264.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '264.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 67423744
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '660.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['60.a1', '132.c1', '220.h1', '330.b1'], 'contains': ['1320.a1'], 'core': '660.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3062, 6542, 4074, 8866], 'generators': [44734985446128011, 6422340100995270, 41772741070013040], 'label': '5280.r.660.a1', 'mobius_quo': 0, 'mobius_sub': 660, 'normal_closure': '660.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['1320.a1'], 'normalizer': '1.a1', 'old_label': '660.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423745
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '660.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '220.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['132.a1', '220.a1', '220.c1', '330.a1', '330.b1', '330.c1'], 'contains': ['1320.a1', '1320.b1', '1320.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [4821, -1, 5054, -1], 'generators': [44734985446128011, 39102834447932290, 41772741070013040], 'label': '5280.r.660.b1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '660.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423746
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '660.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '220.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['132.b1', '220.b1', '220.e1', '330.b1', '330.c1'], 'contains': ['1320.a1', '1320.b1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7795, -1, 5883, -1], 'generators': [5455705447089206, 10842363402478390, 41772741070013040], 'label': '5280.r.660.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '660.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423747
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '660.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['220.d1', '220.f1', '330.a1', '330.c1'], 'contains': ['1320.b1', '1320.c1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 495, 'diagramx': [7290, -1, 6970, -1], 'generators': [5147221894129314, 12052125667637317, 41772741070013040], 'label': '5280.r.660.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1', 'old_label': '660.d1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423748
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '660.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['220.g1', '330.c1'], 'contains': ['1320.b1', '1320.d1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [9048, -1, 8200, -1], 'generators': [4262398886005666, 30035436140984402, 41772741070013040], 'label': '5280.r.660.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '165.a1', 'old_label': '660.e1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 67423749
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '660.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.i1', '220.j1', '330.a1'], 'contains': ['1320.c1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [3980, -1, 4605, -1], 'generators': [12052125667637317, 39102834447932290, 41772741070013040], 'label': '5280.r.660.f1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.a1', 'old_label': '660.f1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 67423750
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.j1', '440.a1', '440.b1', '440.c1', '440.d1', '440.e1'], 'contains': ['1760.a1', '2640.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [5619, -1, 6426, -1], 'generators': [4744352207913140, 41772741070013040], 'label': '5280.r.880.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '880.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '880.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423751
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '880.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '220.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['440.a1', '440.f1'], 'contains': ['1760.a1', '2640.b1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [9719, -1, 7661, -1], 'generators': [24042258004896203, 33405471707136862], 'label': '5280.r.880.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.f1', 'old_label': '880.b1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '880.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423752
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '11.a1'], 'contains': ['44.a1', '110.b1', '132.a1', '220.c1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [4084, -1, 3673, -1], 'generators': [44734985446128011, 39668646791340708, 44697067075260488, 41772741070013040], 'label': '5280.r.22.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1', 'old_label': '22.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1', 'subgroup_fusion': None, 'weyl_group': '120.35'}
  • id: 67423753
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '880.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['440.b1', '440.f1'], 'contains': ['1760.a1', '2640.b1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 660, 'diagramx': [8801, -1, 7281, -1], 'generators': [29950988370754982, 13556750675449154], 'label': '5280.r.880.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.e1', 'old_label': '880.c1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '880.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 67423754
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '1056.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '132.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '528.a1', '528.b1'], 'contains': ['5280.a1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 66, 'diagramx': [1454, -1, 2952, -1], 'generators': [32935044166904759], 'label': '5280.r.1056.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '66.a1', 'old_label': '1056.a1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1056.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423755
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '1320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['120.a1', '264.b1', '440.c1', '660.a1', '660.b1', '660.c1'], 'contains': ['2640.a1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3988, 6542, 4899, 8866], 'generators': [44734985446128011, 41772741070013040], 'label': '5280.r.1320.a1', 'mobius_quo': 0, 'mobius_sub': -660, 'normal_closure': '1320.a1', 'normal_contained_in': ['2.a1', '660.a1'], 'normal_contains': ['2640.a1'], 'normalizer': '1.a1', 'old_label': '1320.a1', 'projective_image': '2640.bt', 'quotient_action_image': '2.1', 'quotient_action_kernel': '660.13', 'quotient_action_kernel_order': 660, 'quotient_fusion': None, 'short_label': '1320.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423756
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '1320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['264.a1', '440.a1', '440.b1', '660.b1', '660.c1', '660.d1', '660.e1'], 'contains': ['2640.a1', '2640.b1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 165, 'diagramx': [7582, -1, 6949, -1], 'generators': [4262398886005666, 41772741070013040], 'label': '5280.r.1320.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '1320.b1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423757
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '1320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['264.c1', '440.d1', '440.e1', '660.b1', '660.d1', '660.f1'], 'contains': ['2640.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [4266, -1, 5209, -1], 'generators': [39102834447932290, 41772741070013040], 'label': '5280.r.1320.c1', 'mobius_quo': None, 'mobius_sub': -36, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '1320.c1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423758
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '1320.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['440.f1', '660.e1'], 'contains': ['2640.b1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 1320, 'diagramx': [9079, -1, 8200, -1], 'generators': [4262398886005666, 30035436140984402], 'label': '5280.r.1320.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '660.e1', 'old_label': '1320.d1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67423759
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '1760.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['880.a1', '880.b1', '880.c1'], 'contains': ['5280.a1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [8867, -1, 6793, -1], 'generators': [4744352207913140], 'label': '5280.r.1760.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1', 'old_label': '1760.a1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1760.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 67423760
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '2640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['240.a1', '528.a1', '880.a1', '1320.a1', '1320.b1', '1320.c1'], 'contains': ['5280.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4123, 6542, 5054, 8866], 'generators': [41772741070013040], 'label': '5280.r.2640.a1', 'mobius_quo': -1, 'mobius_sub': 1320, 'normal_closure': '2640.a1', 'normal_contained_in': ['4.a1', '1320.a1'], 'normal_contains': ['5280.a1'], 'normalizer': '1.a1', 'old_label': '2640.a1', 'projective_image': '2640.bt', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2640.bt', 'quotient_action_kernel_order': 2640, 'quotient_fusion': None, 'short_label': '2640.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67423761
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '2640.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['528.b1', '880.b1', '880.c1', '1320.b1', '1320.d1'], 'contains': ['5280.a1'], 'core': '5280.a1', 'coset_action_label': None, 'count': 330, 'diagramx': [8111, -1, 7113, -1], 'generators': [4262398886005666], 'label': '5280.r.2640.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.f1', 'old_label': '2640.b1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2640.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67423762
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '5280.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['480.a1', '1056.a1', '1760.a1', '2640.a1', '2640.b1'], 'contains': [], 'core': '5280.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4123, 6542, 5054, 8866], 'generators': [], 'label': '5280.r.5280.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '5280.a1', 'normal_contained_in': ['2640.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5280.a1', 'projective_image': '5280.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5280.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67423763
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1320.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '12.a1'], 'contains': ['48.a1', '120.a1', '264.b1'], 'core': '1320.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1273, -1, 380, -1], 'generators': [6422340100995270, 19082840468861376, 2277783661067801, 41772741070013040], 'label': '5280.r.24.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '24.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '110.2'}
  • id: 67423764
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '22.a1'], 'contains': ['220.j1', '264.c1', '440.e1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [3591, -1, 3189, -1], 'generators': [10429050647755529, 15039368961340755, 41772741070013040], 'label': '5280.r.44.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1', 'old_label': '44.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
  • id: 67423765
    {'ambient': '5280.r', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '660.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '24.a1'], 'contains': ['96.a1', '240.a1', '528.a1'], 'core': '2640.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1273, -1, 1407, -1], 'generators': [38318203479259842, 19082840468861376, 41772741070013040], 'label': '5280.r.48.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '48.a1', 'projective_image': '2640.bt', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}