Abstract group data - 540.27

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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': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [2, 6, 2, 4, 6, 6, 5], 'aut_gens': [[1, 4, 12, 36], [1, 4, 24, 532], [365, 28, 12, 156], [3, 4, 12, 144], [1, 4, 12, 468], [5, 4, 12, 156], [1, 364, 12, 144], [325, 4, 12, 36]], 'aut_group': '17280.fp', 'aut_hash': 7336759155281172877, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17280, 'aut_permdeg': 90, 'aut_perms': [1023763962611959781027791650282679715377351253429410689975462718884282286208292176440755027701761460748640919960250514035987552672848905279, 1031101072528116501943692081726729357736249119135886972252166602276939850234080453103735525138198986402584061852491811008727837244126775325, 51024611884510694657448714462650596418147277150258261680004821120934748957031146453046537058924116502414090437501747528116358247327994225, 1353840641146682824115356278799164776678926051591601303258846849329068556619476915401038171712235644630758899702726525641489362073511100924, 1209573547750183568076226508335271633129881523292070641207756405370885960663345059677355715153635067631342783114410531947101656024142842156, 908149092302302895070528295299288508642585767226392166313916302589057183322198426859419371740231710791553256593558425587125997514321145656, 1366035271062582865640514163411686293070382285663412711732727351967498275854613482976506149687594705775568183211891322715013139029938061056], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 6, 4, 1], [4, 45, 2, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 6, 4, 1], [10, 2, 2, 1], [12, 45, 4, 1], [15, 2, 4, 1], [15, 6, 16, 1], [30, 2, 4, 1], [30, 6, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{30}:C_{12}:\\GL(2,3)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '8640.be', 'autcentquo_hash': 9203803121985669655, 'autcentquo_nilpotent': False, 'autcentquo_order': 8640, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 6, 4], [4, 45, 2], [5, 2, 2], [6, 1, 2], [6, 6, 4], [10, 2, 2], [12, 45, 4], [15, 2, 4], [15, 6, 16], [30, 2, 4], [30, 6, 16]], 'center_label': '6.2', 'center_order': 6, 'central_product': False, 'central_quotient': '90.9', 'commutator_count': 2, 'commutator_label': '135.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 27, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 6, 1, 4], [4, 45, 2, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 6, 1, 4], [10, 2, 2, 1], [12, 45, 4, 1], [15, 2, 4, 1], [15, 6, 4, 4], [30, 2, 4, 1], [30, 6, 4, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4536, 'exponent': 60, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[6, 0, 4]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '90.9', 'hash': 27, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 3, 1, 15], 'inner_gens': [[1, 8, 12, 528], [9, 4, 12, 60], [1, 4, 12, 36], [85, 16, 12, 36]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 90, 'inner_split': False, 'inner_tex': 'C_3:D_{15}', 'inner_used': [1, 2, 4], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 44], [3, 8], [6, 8]], 'label': '540.27', 'linC_count': 216, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 36, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C5*He3):C4', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 64, 'number_divisions': 26, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': 30, 'number_subgroup_classes': 66, 'number_subgroups': 334, 'old_label': None, 'order': 540, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [3, 26], [4, 90], [5, 4], [6, 26], [10, 4], [12, 180], [15, 104], [30, 104]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 6, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 1, 0], 'outer_gens': [[1, 4, 24, 424], [3, 192, 12, 412], [1, 380, 12, 52], [1, 184, 12, 80], [1, 192, 12, 232]], 'outer_group': '192.1480', 'outer_hash': 1480, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 18, 'outer_perms': [10606661091000, 9290820271705, 3824144501993280, 3047818433428800, 777130521924984], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3):C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [4, 2], [6, 2], [8, 8], [12, 1], [24, 2]], 'representations': {'PC': {'code': 5917418327232188704428119, 'gens': [1, 3, 4, 5], 'pres': [6, -2, -2, -3, -3, 3, -5, 12, 146, 15844, 466, 118, 15557]}, 'Perm': {'d': 18, 'gens': [43172494046769, 16, 64363528454400, 400168514592000, 50520, 778439913753600]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_5\\times \\He_3):C_4', 'transitive_degree': 180, '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: 138641272
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 27, 'group_order': 540, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 138641283
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 27, 'group_order': 540, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 2, 'size': 1}
  • id: 138641294
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 27, 'group_order': 540, 'label': '3A1', 'order': 3, 'powers': [4, 1, 4], 'representative': 12, 'size': 1}
  • id: 138641305
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 27, 'group_order': 540, 'label': '3A-1', 'order': 3, 'powers': [3, 1, 3], 'representative': 24, 'size': 1}
  • id: 138641316
    {'aut_label': '3B', 'centralizer': '6.a1.a1', 'counter': 5, 'group_counter': 27, 'group_order': 540, 'label': '3B', 'order': 3, 'powers': [5, 1, 5], 'representative': 360, 'size': 6}
  • id: 138641327
    {'aut_label': '3B', 'centralizer': '6.a1.b1', 'counter': 6, 'group_counter': 27, 'group_order': 540, 'label': '3C', 'order': 3, 'powers': [6, 1, 6], 'representative': 4, 'size': 6}
  • id: 138641333
    {'aut_label': '3B', 'centralizer': '6.a1.c1', 'counter': 7, 'group_counter': 27, 'group_order': 540, 'label': '3D', 'order': 3, 'powers': [7, 1, 7], 'representative': 364, 'size': 6}
  • id: 138641334
    {'aut_label': '3B', 'centralizer': '6.a1.d1', 'counter': 8, 'group_counter': 27, 'group_order': 540, 'label': '3E', 'order': 3, 'powers': [8, 1, 8], 'representative': 184, 'size': 6}
  • id: 138641335
    {'aut_label': '4A1', 'centralizer': '45.a1.a1', 'counter': 9, 'group_counter': 27, 'group_order': 540, 'label': '4A1', 'order': 4, 'powers': [2, 10, 9], 'representative': 171, 'size': 45}
  • id: 138641273
    {'aut_label': '4A1', 'centralizer': '45.a1.a1', 'counter': 10, 'group_counter': 27, 'group_order': 540, 'label': '4A-1', 'order': 4, 'powers': [2, 9, 10], 'representative': 169, 'size': 45}
  • id: 138641274
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 27, 'group_order': 540, 'label': '5A1', 'order': 5, 'powers': [12, 12, 1], 'representative': 108, 'size': 2}
  • id: 138641275
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 27, 'group_order': 540, 'label': '5A2', 'order': 5, 'powers': [11, 11, 1], 'representative': 216, 'size': 2}
  • id: 138641276
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 27, 'group_order': 540, 'label': '6A1', 'order': 6, 'powers': [3, 2, 14], 'representative': 26, 'size': 1}
  • id: 138641277
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 27, 'group_order': 540, 'label': '6A-1', 'order': 6, 'powers': [4, 2, 13], 'representative': 14, 'size': 1}
  • id: 138641278
    {'aut_label': '6B', 'centralizer': '6.a1.a1', 'counter': 15, 'group_counter': 27, 'group_order': 540, 'label': '6B', 'order': 6, 'powers': [5, 2, 15], 'representative': 182, 'size': 6}
  • id: 138641279
    {'aut_label': '6B', 'centralizer': '6.a1.b1', 'counter': 16, 'group_counter': 27, 'group_order': 540, 'label': '6C', 'order': 6, 'powers': [6, 2, 16], 'representative': 10, 'size': 6}
  • id: 138641280
    {'aut_label': '6B', 'centralizer': '6.a1.c1', 'counter': 17, 'group_counter': 27, 'group_order': 540, 'label': '6D', 'order': 6, 'powers': [7, 2, 17], 'representative': 214, 'size': 6}
  • id: 138641281
    {'aut_label': '6B', 'centralizer': '6.a1.d1', 'counter': 18, 'group_counter': 27, 'group_order': 540, 'label': '6E', 'order': 6, 'powers': [8, 2, 18], 'representative': 382, 'size': 6}
  • id: 138641282
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 19, 'group_counter': 27, 'group_order': 540, 'label': '10A1', 'order': 10, 'powers': [11, 20, 2], 'representative': 326, 'size': 2}
  • id: 138641284
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 20, 'group_counter': 27, 'group_order': 540, 'label': '10A3', 'order': 10, 'powers': [12, 19, 2], 'representative': 434, 'size': 2}
  • id: 138641285
    {'aut_label': '12A1', 'centralizer': '45.a1.a1', 'counter': 21, 'group_counter': 27, 'group_order': 540, 'label': '12A1', 'order': 12, 'powers': [13, 9, 23], 'representative': 145, 'size': 45}
  • id: 138641286
    {'aut_label': '12A1', 'centralizer': '45.a1.a1', 'counter': 22, 'group_counter': 27, 'group_order': 540, 'label': '12A-1', 'order': 12, 'powers': [14, 10, 24], 'representative': 159, 'size': 45}
  • id: 138641287
    {'aut_label': '12A1', 'centralizer': '45.a1.a1', 'counter': 23, 'group_counter': 27, 'group_order': 540, 'label': '12A5', 'order': 12, 'powers': [14, 9, 21], 'representative': 157, 'size': 45}
  • id: 138641288
    {'aut_label': '12A1', 'centralizer': '45.a1.a1', 'counter': 24, 'group_counter': 27, 'group_order': 540, 'label': '12A-5', 'order': 12, 'powers': [13, 10, 22], 'representative': 147, 'size': 45}
  • id: 138641289
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 25, 'group_counter': 27, 'group_order': 540, 'label': '15A1', 'order': 15, 'powers': [27, 11, 3], 'representative': 240, 'size': 2}
  • id: 138641290
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 27, 'group_order': 540, 'label': '15A-1', 'order': 15, 'powers': [28, 11, 4], 'representative': 336, 'size': 2}
  • id: 138641291
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 27, 'group_order': 540, 'label': '15A2', 'order': 15, 'powers': [25, 12, 4], 'representative': 444, 'size': 2}
  • id: 138641292
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 27, 'group_order': 540, 'label': '15A-2', 'order': 15, 'powers': [26, 12, 3], 'representative': 132, 'size': 2}
  • id: 138641293
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 29, 'group_counter': 27, 'group_order': 540, 'label': '15B1', 'order': 15, 'powers': [30, 12, 5], 'representative': 72, 'size': 6}
  • id: 138641295
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 30, 'group_counter': 27, 'group_order': 540, 'label': '15B2', 'order': 15, 'powers': [31, 11, 5], 'representative': 144, 'size': 6}
  • id: 138641296
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 31, 'group_counter': 27, 'group_order': 540, 'label': '15B4', 'order': 15, 'powers': [32, 12, 5], 'representative': 288, 'size': 6}
  • id: 138641297
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 32, 'group_counter': 27, 'group_order': 540, 'label': '15B7', 'order': 15, 'powers': [29, 11, 5], 'representative': 504, 'size': 6}
  • id: 138641298
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 33, 'group_counter': 27, 'group_order': 540, 'label': '15C1', 'order': 15, 'powers': [34, 11, 6], 'representative': 224, 'size': 6}
  • id: 138641299
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 34, 'group_counter': 27, 'group_order': 540, 'label': '15C2', 'order': 15, 'powers': [35, 12, 6], 'representative': 436, 'size': 6}
  • id: 138641300
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 35, 'group_counter': 27, 'group_order': 540, 'label': '15C4', 'order': 15, 'powers': [36, 11, 6], 'representative': 332, 'size': 6}
  • id: 138641301
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 36, 'group_counter': 27, 'group_order': 540, 'label': '15C7', 'order': 15, 'powers': [33, 12, 6], 'representative': 440, 'size': 6}
  • id: 138641302
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 37, 'group_counter': 27, 'group_order': 540, 'label': '15D1', 'order': 15, 'powers': [38, 12, 7], 'representative': 104, 'size': 6}
  • id: 138641303
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 38, 'group_counter': 27, 'group_order': 540, 'label': '15D2', 'order': 15, 'powers': [39, 11, 7], 'representative': 148, 'size': 6}
  • id: 138641304
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 39, 'group_counter': 27, 'group_order': 540, 'label': '15D4', 'order': 15, 'powers': [40, 12, 7], 'representative': 320, 'size': 6}
  • id: 138641306
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 40, 'group_counter': 27, 'group_order': 540, 'label': '15D7', 'order': 15, 'powers': [37, 11, 7], 'representative': 536, 'size': 6}
  • id: 138641307
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 41, 'group_counter': 27, 'group_order': 540, 'label': '15E1', 'order': 15, 'powers': [42, 11, 8], 'representative': 164, 'size': 6}
  • id: 138641308
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 42, 'group_counter': 27, 'group_order': 540, 'label': '15E2', 'order': 15, 'powers': [43, 12, 8], 'representative': 292, 'size': 6}
  • id: 138641309
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 43, 'group_counter': 27, 'group_order': 540, 'label': '15E4', 'order': 15, 'powers': [44, 11, 8], 'representative': 56, 'size': 6}
  • id: 138641310
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 44, 'group_counter': 27, 'group_order': 540, 'label': '15E7', 'order': 15, 'powers': [41, 12, 8], 'representative': 488, 'size': 6}
  • id: 138641311
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 45, 'group_counter': 27, 'group_order': 540, 'label': '30A1', 'order': 30, 'powers': [25, 19, 13], 'representative': 122, 'size': 2}
  • id: 138641312
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 46, 'group_counter': 27, 'group_order': 540, 'label': '30A-1', 'order': 30, 'powers': [26, 19, 14], 'representative': 134, 'size': 2}
  • id: 138641313
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 47, 'group_counter': 27, 'group_order': 540, 'label': '30A7', 'order': 30, 'powers': [28, 20, 13], 'representative': 230, 'size': 2}
  • id: 138641314
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 48, 'group_counter': 27, 'group_order': 540, 'label': '30A-7', 'order': 30, 'powers': [27, 20, 14], 'representative': 242, 'size': 2}
  • id: 138641315
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 49, 'group_counter': 27, 'group_order': 540, 'label': '30B1', 'order': 30, 'powers': [29, 20, 15], 'representative': 38, 'size': 6}
  • id: 138641317
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 50, 'group_counter': 27, 'group_order': 540, 'label': '30B7', 'order': 30, 'powers': [32, 19, 15], 'representative': 254, 'size': 6}
  • id: 138641318
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 51, 'group_counter': 27, 'group_order': 540, 'label': '30B11', 'order': 30, 'powers': [31, 20, 15], 'representative': 146, 'size': 6}
  • id: 138641319
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 52, 'group_counter': 27, 'group_order': 540, 'label': '30B13', 'order': 30, 'powers': [30, 19, 15], 'representative': 74, 'size': 6}
  • id: 138641320
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 53, 'group_counter': 27, 'group_order': 540, 'label': '30C1', 'order': 30, 'powers': [33, 19, 16], 'representative': 114, 'size': 6}
  • id: 138641321
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 54, 'group_counter': 27, 'group_order': 540, 'label': '30C7', 'order': 30, 'powers': [36, 20, 16], 'representative': 222, 'size': 6}
  • id: 138641322
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 55, 'group_counter': 27, 'group_order': 540, 'label': '30C11', 'order': 30, 'powers': [35, 19, 16], 'representative': 118, 'size': 6}
  • id: 138641323
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 56, 'group_counter': 27, 'group_order': 540, 'label': '30C13', 'order': 30, 'powers': [34, 20, 16], 'representative': 330, 'size': 6}
  • id: 138641324
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 57, 'group_counter': 27, 'group_order': 540, 'label': '30D1', 'order': 30, 'powers': [37, 20, 17], 'representative': 42, 'size': 6}
  • id: 138641325
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 58, 'group_counter': 27, 'group_order': 540, 'label': '30D7', 'order': 30, 'powers': [40, 19, 17], 'representative': 258, 'size': 6}
  • id: 138641326
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 59, 'group_counter': 27, 'group_order': 540, 'label': '30D11', 'order': 30, 'powers': [39, 20, 17], 'representative': 150, 'size': 6}
  • id: 138641328
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 60, 'group_counter': 27, 'group_order': 540, 'label': '30D13', 'order': 30, 'powers': [38, 19, 17], 'representative': 82, 'size': 6}
  • id: 138641329
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 61, 'group_counter': 27, 'group_order': 540, 'label': '30E1', 'order': 30, 'powers': [41, 19, 18], 'representative': 78, 'size': 6}
  • id: 138641330
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 62, 'group_counter': 27, 'group_order': 540, 'label': '30E7', 'order': 30, 'powers': [44, 20, 18], 'representative': 46, 'size': 6}
  • id: 138641331
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 63, 'group_counter': 27, 'group_order': 540, 'label': '30E11', 'order': 30, 'powers': [43, 19, 18], 'representative': 294, 'size': 6}
  • id: 138641332
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 64, 'group_counter': 27, 'group_order': 540, 'label': '30E13', 'order': 30, 'powers': [42, 20, 18], 'representative': 154, 'size': 6}
• 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: 12291722
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12291733
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12291741
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
  • id: 12291742
    {'cdim': 2, 'counter': 4, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -1, 2, 0, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1], 'schur_index': 1}
  • id: 12291743
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, 0, 0, 2, 2, 2, 2, -1, -1, 2, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 2, 2, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12291744
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, 0, 0, 2, 2, 2, 2, -1, 2, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12291745
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, 2], 'schur_index': 1}
  • id: 12291746
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2e', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -1, -1, -1, 2, 0, 0, 2, 2, -2, -2, 1, 1, 1, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, -2, 1], 'schur_index': 2}
  • id: 12291747
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2f', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -1, -1, 2, -1, 0, 0, 2, 2, -2, -2, 1, 1, -2, 1, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -2, -2, -2, -2, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 2}
  • id: 12291723
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2g', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -1, 2, -1, -1, 0, 0, 2, 2, -2, -2, 1, -2, 1, 1, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 2}
  • id: 12291724
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2h', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, -1, -1, -1, 0, 0, 2, 2, -2, -2, -2, 1, 1, 1, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, -2], 'schur_index': 2}
  • id: 12291725
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2i', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 0, 0, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12291726
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2j', 'multiplicity': 2, 'nt': [20, 2], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, 4, 4, 4, 0, 0, -1, -1, -4, -4, -4, -4, -4, -4, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 2}
  • id: 12291736
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.3a', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 0, 0, 0, 0, 2, 2, 6, 6, -3, -3, 0, 0, 0, 0, 6, 6, -1, -1, -1, -1, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12291737
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.3b', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 0, 0, 0, 0, -2, -2, 6, 6, -3, -3, 0, 0, 0, 0, 6, 6, 1, 1, 1, 1, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12291727
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2k', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, -4, -4, 8, 0, 0, -2, -2, 8, 8, -4, -4, -4, 8, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, -2, 1], 'schur_index': 1}
  • id: 12291728
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2l', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, -4, 8, -4, 0, 0, -2, -2, 8, 8, -4, -4, 8, -4, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, -2, -2, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12291729
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2m', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, 8, -4, -4, 0, 0, -2, -2, 8, 8, -4, 8, -4, -4, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12291730
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2n', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, -4, -4, -4, 0, 0, -2, -2, 8, 8, 8, -4, -4, -4, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, -2, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1, -2], 'schur_index': 1}
  • id: 12291731
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2o', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 8, 'qvalues': [8, -8, 8, 8, -4, -4, -4, 8, 0, 0, -2, -2, -8, -8, 4, 4, 4, -8, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1], 'schur_index': 2}
  • id: 12291732
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2p', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 8, 'qvalues': [8, -8, 8, 8, -4, -4, 8, -4, 0, 0, -2, -2, -8, -8, 4, 4, -8, 4, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 2, 2, 2, 2, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 2}
  • id: 12291734
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2q', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 8, 'qvalues': [8, -8, 8, 8, -4, 8, -4, -4, 0, 0, -2, -2, -8, -8, 4, -8, 4, 4, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 2, 2, 2, 2, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 2}
  • id: 12291735
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.2r', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 8, 'qvalues': [8, -8, 8, 8, 8, -4, -4, -4, 0, 0, -2, -2, -8, -8, -8, 4, 4, 4, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, -2, 1, 1, 1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, 2], 'schur_index': 2}
  • id: 12291738
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.3c', 'multiplicity': 4, 'nt': [36, 78], 'qdim': 12, 'qvalues': [12, -12, -6, -6, 0, 0, 0, 0, 0, 0, 12, 12, 6, 6, 0, 0, 0, 0, -12, -12, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12291739
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.6a', 'multiplicity': 4, 'nt': [45, 31], 'qdim': 24, 'qvalues': [24, 24, -12, -12, 0, 0, 0, 0, 0, 0, -6, -6, -12, -12, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12291740
    {'cdim': 6, 'counter': 26, 'faithful': True, 'group': '540.27', 'group_order': 540, 'image': None, 'label': '540.27.6b', 'multiplicity': 4, 'nt': [180, 0], 'qdim': 24, 'qvalues': [24, -24, -12, -12, 0, 0, 0, 0, 0, 0, -6, -6, 12, 12, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 28517312
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 540, 'label': '540.27.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 28517323
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 270, 'label': '540.27.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 28517334
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 135, 'label': '540.27.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 28517345
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 135, 'label': '540.27.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 28517356
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 90, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.b1', 'kernel_order': 90, 'label': '540.27.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]]]}
  • id: 28517367
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 90, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 90, 'label': '540.27.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 28517373
    {'center': '6.a1.d1', 'center_index': 6, 'center_order': 90, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.d1', 'kernel_order': 90, 'label': '540.27.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 28517374
    {'center': '6.a1.c1', 'center_index': 6, 'center_order': 90, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.c1', 'kernel_order': 90, 'label': '540.27.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
  • id: 28517375
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 90, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.b1', 'kernel_order': 45, 'label': '540.27.2e', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]]]}
  • id: 28517313
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 90, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 45, 'label': '540.27.2f', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 28517314
    {'center': '6.a1.d1', 'center_index': 6, 'center_order': 90, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.d1', 'kernel_order': 45, 'label': '540.27.2g', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 28517315
    {'center': '6.a1.c1', 'center_index': 6, 'center_order': 90, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.c1', 'kernel_order': 45, 'label': '540.27.2h', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]]]}
  • id: 28517316
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 13, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 54, 'label': '540.27.2i1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 28517317
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 14, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 54, 'label': '540.27.2i2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 28517318
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 15, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.a1.a1', 'kernel_order': 27, 'label': '540.27.2j1', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
  • id: 28517319
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 16, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.a1.a1', 'kernel_order': 27, 'label': '540.27.2j2', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
  • id: 28517320
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 17, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.27.2k1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
  • id: 28517321
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 18, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.27.2k2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]]]}
  • id: 28517322
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 19, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.27.2k3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]]]}
  • id: 28517324
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 20, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.27.2k4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 7], [1, -7]]]}
  • id: 28517325
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 21, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.27.2l1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 4], [1, -4]]]}
  • id: 28517326
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 22, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.27.2l2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 1], [1, -1]]]}
  • id: 28517327
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 23, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.27.2l3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 7], [1, -7]]]}
  • id: 28517328
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 24, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.27.2l4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
  • id: 28517329
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 25, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.27.2m1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 4], [1, -4]]]}
  • id: 28517330
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 26, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.27.2m2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
  • id: 28517331
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 27, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.27.2m3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 7], [1, -7]]]}
  • id: 28517332
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 28, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.27.2m4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]]]}
  • id: 28517333
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 29, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.27.2n1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]]]}
  • id: 28517335
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 30, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.27.2n2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]]]}
  • id: 28517336
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 31, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.27.2n3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
  • id: 28517337
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  • id: 28517338
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  • id: 28517339
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 34, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '60.3', 'image_order': 60, 'indicator': -1, 'kernel': '60.a1.b1', 'kernel_order': 9, 'label': '540.27.2o2', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]]]}
  • id: 28517340
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 35, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '60.3', 'image_order': 60, 'indicator': -1, 'kernel': '60.a1.b1', 'kernel_order': 9, 'label': '540.27.2o3', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]]]}
  • id: 28517341
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  • id: 28517342
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  • id: 28517343
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  • id: 28517344
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 39, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '60.3', 'image_order': 60, 'indicator': -1, 'kernel': '60.a1.a1', 'kernel_order': 9, 'label': '540.27.2p3', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]]]}
  • id: 28517346
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  • id: 28517347
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  • id: 28517348
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  • id: 28517349
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  • id: 28517350
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  • id: 28517351
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  • id: 28517352
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  • id: 28517353
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  • id: 28517354
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  • id: 28517355
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  • id: 28517357
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  • id: 28517358
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 51, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 10, 'label': '540.27.3b1', 'nt': [18, 24], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517359
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 52, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 10, 'label': '540.27.3b2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517360
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 53, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.27.3c1', 'nt': [36, 78], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[3, 0]], [[3, 0]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517361
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 54, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.27.3c2', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[3, 0]], [[3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[3, 4]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517362
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 55, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.27.3c3', 'nt': [36, 78], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[3, 0]], [[3, 0]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-3, 2]], [[-3, 2]], [[3, 4]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517363
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 56, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '108.11', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.27.3c4', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[3, 0]], [[3, 0]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[3, 4]], [[3, 4]], [[-3, 2]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517364
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 57, 'cyclotomic_n': 15, 'dim': 6, 'faithful': False, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.27.6a1', 'nt': [45, 31], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, -5]], [[6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[6, 5]], [[6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 1], [3, 4]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 4]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517365
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 58, 'cyclotomic_n': 15, 'dim': 6, 'faithful': False, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.27.6a2', 'nt': [45, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 5]], [[6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[6, -5]], [[6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 1], [3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 1], [3, 4]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517366
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 59, 'cyclotomic_n': 15, 'dim': 6, 'faithful': False, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.27.6a3', 'nt': [45, 31], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, -5]], [[6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[6, 5]], [[6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 4]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 1], [3, 4]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517368
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 60, 'cyclotomic_n': 15, 'dim': 6, 'faithful': False, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.27.6a4', 'nt': [45, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 5]], [[6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[6, -5]], [[6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 1], [3, 4]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 1], [3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517369
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 61, 'cyclotomic_n': 15, 'dim': 6, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '540.27', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.27.6b1', 'nt': [180, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, -5]], [[6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[-6, 5]], [[-6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 3], [-3, -3]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 1], [3, 4]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, 4]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [3, 7]], [[-3, 0], [3, 1], [3, 4], [-3, 5]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [3, 5], [-3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517370
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 62, 'cyclotomic_n': 15, 'dim': 6, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '540.27', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.27.6b2', 'nt': [180, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 5]], [[6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[-6, -5]], [[-6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 3], [-3, -3]], [[-3, 6], [-3, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 1], [3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [3, 7]], [[-3, 1], [-3, 4]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [3, 5], [-3, 7]], [[-3, 0], [3, 1], [3, 4], [-3, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517371
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 63, 'cyclotomic_n': 15, 'dim': 6, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '540.27', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.27.6b3', 'nt': [180, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, -5]], [[6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[-6, 5]], [[-6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6], [-3, -6]], [[-3, 3], [-3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, 4]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [3, 1], [3, 4], [-3, 5]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [3, 5], [-3, 7]], [[-3, 1], [-3, 4]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 28517372
    {'center': '90.a1.a1', 'center_index': 90, 'center_order': 6, 'counter': 64, 'cyclotomic_n': 15, 'dim': 6, 'faithful': True, 'field': [1, 1, 2, -1, 1], 'group': '540.27', 'group_counter': 27, 'group_order': 540, 'image': None, 'image_isoclass': '540.27', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.27.6b4', 'nt': [180, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 5]], [[6, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[-6, -5]], [[-6, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6], [-3, -6]], [[-3, 3], [-3, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 1], [3, 4]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [3, 5], [-3, 7]], [[-3, 0], [3, 1], [3, 4], [-3, 5]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [3, 7]], [[-3, 1], [-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 108120946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 540, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '540.27.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '540.27', 'subgroup_hash': 27, 'subgroup_order': 540, 'subgroup_tex': '(C_5\\times \\He_3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108120957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 270, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '270.21', 'subgroup_hash': 21, 'subgroup_order': 270, 'subgroup_tex': 'C_{10}\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 108120968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.15', 'subgroup_hash': 15, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.3.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.15', 'subgroup_hash': 15, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.3.a1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.15', 'subgroup_hash': 15, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108121001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.3.a1.d1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.15', 'subgroup_hash': 15, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108121009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 135, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 15, 'label': '540.27.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '135.3', 'subgroup_hash': 3, 'subgroup_order': 135, 'subgroup_tex': 'C_5\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 108121010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '540.27.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108121011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120947
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120948
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.6.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120949
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.6.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '90.10', 'subgroup_hash': 10, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120950
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120951
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108120952
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.9.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108120953
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.9.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108120954
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.9.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108120955
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 108120956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120959
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.12.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120960
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.12.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.15.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.15.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.15.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 108120965
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 30, 'counter': 27, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.27.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120966
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120967
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120969
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.18.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120970
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.18.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108120971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 27, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '540.27.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 108120972
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '540.27.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 108120973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{15}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.30.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{15}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.30.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{15}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120976
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.30.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{15}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 15, 'counter': 38, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.27.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120980
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.36.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120981
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.36.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120982
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.36.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108120983
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '45.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': 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: 108120984
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.45.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': 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: 108120985
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.45.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': 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: 108120986
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.45.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': 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: 108120987
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.27.45.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': 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: 108120988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 10, 'counter': 48, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.27.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 108120989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 108120991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.60.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 108120992
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.60.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 108120993
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.27.60.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 108120994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 6, 'counter': 53, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.27.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '90.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 90, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{15}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.90.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.90.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.90.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108120999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 5, 'counter': 58, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '540.27.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3:C_4', 'simple': True, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 108121000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '540.27.135.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '135.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 135, 'quotient_simple': 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': 2}
  • id: 108121002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 3, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.27.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '180.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '180.17', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 180, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_{15}', 'simple': True, 'solvable': True, 'special_labels': ['D2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 108121003
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 108121004
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.180.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 108121005
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.180.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 108121006
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.27.180.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 108121007
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 2, 'counter': 65, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.27.270.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '270.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '270.19', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 19, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 270, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_{15}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 108121008
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.27', 'ambient_counter': 27, 'ambient_order': 540, 'ambient_tex': '(C_5\\times \\He_3):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 1, 'counter': 66, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '540.27.540.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '540.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '540.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 540, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_5\\times \\He_3):C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C6'], '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: 108120946
    {'ambient': '540.27', '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': '90.a1.a1', 'complements': ['540.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.a1.b1', '3.a1.c1', '3.a1.d1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5739, 3485, 6704, 4625, 4751, 5282, 6651, 5219], 'generators': [1, 12, 4, 360, 2, 108], 'label': '540.27.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '90.9'}
  • id: 108120947
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.b1'], 'contains': ['12.a1.b1', '18.a1.a1', '18.b1.b1', '30.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4479, 5797, 5114, 6398, 4659, 8635, 4707, 4613], 'generators': [2, 12, 108, 4], 'label': '540.27.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.b1', '18.a1.a1', '30.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120948
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.c1'], 'contains': ['12.a1.c1', '18.a1.a1', '18.b1.c1', '30.a1.c1'], 'core': '6.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4479, 5797, 5907, 624, 4659, 8635, 2098, 7049], 'generators': [2, 12, 108, 364], 'label': '540.27.6.a1.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.c1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.c1', '18.a1.a1', '30.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.c1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120949
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.d1'], 'contains': ['12.a1.d1', '18.a1.a1', '18.b1.d1', '30.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4479, 5797, 2970, 8463, 4659, 8635, 2722, 5831], 'generators': [2, 12, 108, 184], 'label': '540.27.6.a1.d1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.d1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.d1', '18.a1.a1', '30.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.d1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120950
    {'ambient': '540.27', 'aut_centralizer_order': 24, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '80.50', 'aut_weyl_index': 216, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.a1.b1', '3.a1.c1', '3.a1.d1'], 'contains': ['18.a1.a1', '27.a1.a1', '45.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9123, -1, 7932, -1, 9243, -1, 6888, -1], 'generators': [1, 2, 108, 12], 'label': '540.27.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 108120951
    {'ambient': '540.27', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.b1.a1', '27.a1.a1', '45.b1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6084, -1, 7223, -1, 7790, -1, 8074, -1], 'generators': [1, 192, 108, 2], 'label': '540.27.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '9.b1.a1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108120952
    {'ambient': '540.27', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.b1'], 'contains': ['18.b1.b1', '27.a1.a1', '45.b1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6084, -1, 9280, -1, 7790, -1, 9807, -1], 'generators': [1, 4, 108, 2], 'label': '540.27.9.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '9.b1.b1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.b1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108120953
    {'ambient': '540.27', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.c1'], 'contains': ['18.b1.c1', '27.a1.a1', '45.b1.c1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6084, -1, 9786, -1, 7790, -1, 5247, -1], 'generators': [1, 364, 108, 2], 'label': '540.27.9.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '9.b1.c1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.c1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108120954
    {'ambient': '540.27', 'aut_centralizer_order': 6, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.d1'], 'contains': ['18.b1.d1', '27.a1.a1', '45.b1.d1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6084, -1, 3021, -1, 7790, -1, 6341, -1], 'generators': [1, 184, 108, 2], 'label': '540.27.9.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '9.b1.d1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.d1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108121010
    {'ambient': '540.27', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 20, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '15.a1.a1', '15.a1.b1', '15.a1.c1', '15.a1.d1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5739, -1, 6500, -1, 4751, -1, 7588, -1], 'generators': [1, 12, 2, 4, 360], 'label': '540.27.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108120955
    {'ambient': '540.27', 'aut_centralizer_order': 40, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 40, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.a1.a1', '30.a1.b1', '30.a1.c1', '30.a1.d1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2334, 3485, 3469, 3146, 2851, 5282, 4026, 8379], 'generators': [2, 4, 360, 12], 'label': '540.27.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1', '30.a1.c1', '30.a1.b1', '30.a1.d1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108120956
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.a1', 'complements': ['45.b1.b1', '45.b1.c1', '45.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1932, 3553, 1376, 4652, 2942, 3870, 1524, 542], 'generators': [12, 108, 360], 'label': '540.27.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['36.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120957
    {'ambient': '540.27', 'aut_centralizer_order': 10, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.46191', 'aut_weyl_index': 10, 'centralizer': '18.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.a1.c1', '6.a1.d1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2930, 3485, 4223, 4625, 2942, 5282, 3345, 5219], 'generators': [2, 360, 108, 4, 12], 'label': '540.27.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.c1', '6.a1.b1', '6.a1.d1', '6.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108120958
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.b1', 'complements': ['45.b1.a1', '45.b1.c1', '45.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.b1'], 'contains': ['36.a1.a1', '36.b1.b1', '60.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1932, 3553, 2169, 7370, 2942, 3870, 2427, 1759], 'generators': [4, 108, 12], 'label': '540.27.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.a1', '6.a1.b1'], 'normal_contains': ['36.a1.a1', '60.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120959
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.c1', 'complements': ['45.b1.a1', '45.b1.d1', '45.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.c1'], 'contains': ['36.a1.a1', '36.b1.c1', '60.a1.c1'], 'core': '12.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1932, 3553, 3712, 788, 2942, 3870, 277, 4195], 'generators': [364, 108, 12], 'label': '540.27.12.a1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.c1', 'normal_contained_in': ['4.a1.a1', '6.a1.c1'], 'normal_contains': ['36.a1.a1', '60.a1.c1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.c1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120960
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.d1', 'complements': ['45.b1.a1', '45.b1.b1', '45.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.d1'], 'contains': ['36.a1.a1', '36.b1.d1', '60.a1.d1'], 'core': '12.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1932, 3553, 285, 9436, 2942, 3870, 901, 2977], 'generators': [184, 108, 12], 'label': '540.27.12.a1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.d1', 'normal_contained_in': ['4.a1.a1', '6.a1.d1'], 'normal_contains': ['36.a1.a1', '60.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.d1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120961
    {'ambient': '540.27', 'aut_centralizer_order': 12, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '24.14', 'aut_weyl_index': 720, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '45.a1.a1', '45.b1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7953, -1, 6802, -1, 6336, -1, 8621, -1], 'generators': [1, 360, 2, 192], 'label': '540.27.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120962
    {'ambient': '540.27', 'aut_centralizer_order': 12, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '24.14', 'aut_weyl_index': 720, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.b1', '5.a1.a1'], 'contains': ['30.a1.b1', '45.a1.a1', '45.b1.b1'], 'core': '30.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [7953, -1, 7752, -1, 6336, -1, 9260, -1], 'generators': [1, 12, 2, 4], 'label': '540.27.15.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '15.a1.b1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120963
    {'ambient': '540.27', 'aut_centralizer_order': 12, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '24.14', 'aut_weyl_index': 720, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.c1', '5.a1.a1'], 'contains': ['30.a1.c1', '45.a1.a1', '45.b1.c1'], 'core': '30.a1.c1', 'coset_action_label': None, 'count': 15, 'diagramx': [7953, -1, 8554, -1, 6336, -1, 5794, -1], 'generators': [1, 12, 2, 364], 'label': '540.27.15.a1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.c1', 'old_label': '15.a1.c1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120964
    {'ambient': '540.27', 'aut_centralizer_order': 12, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '24.14', 'aut_weyl_index': 720, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.d1', '5.a1.a1'], 'contains': ['30.a1.d1', '45.a1.a1', '45.b1.d1'], 'core': '30.a1.d1', 'coset_action_label': None, 'count': 15, 'diagramx': [7953, -1, 5703, -1, 6336, -1, 7527, -1], 'generators': [1, 12, 2, 184], 'label': '540.27.15.a1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.d1', 'old_label': '15.a1.d1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120965
    {'ambient': '540.27', 'aut_centralizer_order': 2160, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.a1.b1', '6.a1.c1', '6.a1.d1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.a1.a1', '90.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6324, 7320, 4803, 6811, 6499, 8804, 3766, 5675], 'generators': [2, 108, 12], 'label': '540.27.18.a1.a1', 'mobius_quo': -1, 'mobius_sub': -27, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.c1', '6.a1.b1', '6.a1.d1', '6.a1.a1'], 'normal_contains': ['36.a1.a1', '54.a1.a1', '90.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '90.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120966
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '54.a1.a1', '90.b1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4742, -1, 5523, -1, 5605, -1, 4960, -1], 'generators': [2, 108, 360], 'label': '540.27.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120967
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '9.b1.b1'], 'contains': ['36.b1.b1', '54.a1.a1', '90.b1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4742, -1, 6617, -1, 5605, -1, 6337, -1], 'generators': [2, 108, 4], 'label': '540.27.18.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.b1.b1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120968
    {'ambient': '540.27', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 36, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '9.b1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7517, -1, 7046, -1, 6336, -1, 7022, -1], 'generators': [1, 2, 192, 360, 108], 'label': '540.27.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108120969
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '9.b1.c1'], 'contains': ['36.b1.c1', '54.a1.a1', '90.b1.c1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4742, -1, 7611, -1, 5605, -1, 2909, -1], 'generators': [2, 108, 364], 'label': '540.27.18.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '18.b1.c1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120970
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.d1', '9.b1.d1'], 'contains': ['36.b1.d1', '54.a1.a1', '90.b1.d1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4742, -1, 928, -1, 5605, -1, 4103, -1], 'generators': [2, 108, 184], 'label': '540.27.18.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '18.b1.d1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120971
    {'ambient': '540.27', 'aut_centralizer_order': 40, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 40, 'centralizer': '18.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['60.a1.a1', '60.a1.b1', '60.a1.c1', '60.a1.d1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [591, 1824, 1196, 1966, 1743, 1648, 1976, 5077], 'generators': [4, 360], 'label': '540.27.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['60.a1.c1', '60.a1.b1', '60.a1.d1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '180.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108120972
    {'ambient': '540.27', 'aut_centralizer_order': 48, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '40.12', 'aut_weyl_index': 432, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.b1.b1', '9.b1.c1', '9.b1.d1'], 'contains': ['54.a1.a1', '135.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7506, -1, 9252, -1, 9243, -1, 7033, -1], 'generators': [1, 108, 2], 'label': '540.27.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 108120973
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '90.a1.a1', '90.b1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4020, 5283, 4050, 2715, 4466, 6695, 5388, 6511], 'generators': [2, 12, 360], 'label': '540.27.30.a1.a1', 'mobius_quo': 0, 'mobius_sub': -15, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.a1.a1'], 'normal_contains': ['60.a1.a1', '90.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120974
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '10.a1.a1', '15.a1.b1'], 'contains': ['60.a1.b1', '90.a1.a1', '90.b1.b1'], 'core': '30.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4020, 5283, 4733, 4540, 4466, 6695, 5908, 7527], 'generators': [2, 4, 12], 'label': '540.27.30.a1.b1', 'mobius_quo': 0, 'mobius_sub': -15, 'normal_closure': '30.a1.b1', 'normal_contained_in': ['6.a1.b1', '10.a1.a1'], 'normal_contains': ['60.a1.b1', '90.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.b1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '30.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120975
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.c1', '10.a1.a1', '15.a1.c1'], 'contains': ['60.a1.c1', '90.a1.a1', '90.b1.c1'], 'core': '30.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4020, 5283, 6162, 564, 4466, 6695, 3338, 9559], 'generators': [2, 364, 12], 'label': '540.27.30.a1.c1', 'mobius_quo': 0, 'mobius_sub': -15, 'normal_closure': '30.a1.c1', 'normal_contained_in': ['6.a1.c1', '10.a1.a1'], 'normal_contains': ['60.a1.c1', '90.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.c1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '30.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120976
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.d1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.d1', '10.a1.a1', '15.a1.d1'], 'contains': ['60.a1.d1', '90.a1.a1', '90.b1.d1'], 'core': '30.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [4020, 5283, 3068, 6691, 4466, 6695, 4531, 8543], 'generators': [2, 184, 12], 'label': '540.27.30.a1.d1', 'mobius_quo': 0, 'mobius_sub': -15, 'normal_closure': '30.a1.d1', 'normal_contained_in': ['6.a1.d1', '10.a1.a1'], 'normal_contains': ['60.a1.d1', '90.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.d1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '30.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120977
    {'ambient': '540.27', 'aut_centralizer_order': 2160, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.a1.b1', '12.a1.c1', '12.a1.d1', '18.a1.a1'], 'contains': ['108.a1.a1', '180.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3389, 5591, 1781, 7766, 4792, 5697, 1662, 3216], 'generators': [12, 108], 'label': '540.27.36.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.c1', '12.a1.b1', '12.a1.d1', '12.a1.a1', '18.a1.a1'], 'normal_contains': ['108.a1.a1', '180.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '180.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120978
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.b1.a1'], 'contains': ['108.a1.a1', '180.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1313, -1, 2574, -1, 3897, -1, 2649, -1], 'generators': [360, 108], 'label': '540.27.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120979
    {'ambient': '540.27', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 36, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.b1', '9.a1.a1', '9.b1.b1', '15.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7517, -1, 7808, -1, 6336, -1, 8154, -1], 'generators': [1, 2, 4, 12, 108], 'label': '540.27.3.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '3.a1.b1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.b1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108120980
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '18.b1.b1'], 'contains': ['108.a1.a1', '180.b1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1313, -1, 4553, -1, 3897, -1, 3613, -1], 'generators': [4, 108], 'label': '540.27.36.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.b1.b1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120981
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.c1', '18.b1.c1'], 'contains': ['108.a1.a1', '180.b1.c1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1313, -1, 5346, -1, 3897, -1, 1012, -1], 'generators': [364, 108], 'label': '540.27.36.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '36.b1.c1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120982
    {'ambient': '540.27', 'aut_centralizer_order': 180, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 2160, 'centralizer': '6.a1.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.d1', '18.b1.d1'], 'contains': ['108.a1.a1', '180.b1.d1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1313, -1, 214, -1, 3897, -1, 1999, -1], 'generators': [184, 108], 'label': '540.27.36.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '36.b1.d1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120983
    {'ambient': '540.27', 'aut_centralizer_order': 96, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '4.2', 'aut_weyl_index': 4320, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.a1.a1', '15.a1.b1', '15.a1.c1', '15.a1.d1'], 'contains': ['90.a1.a1', '135.a1.a1'], 'core': '90.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [9409, -1, 8007, -1, 8328, -1, 7729, -1], 'generators': [1, 12, 2], 'label': '540.27.45.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108120984
    {'ambient': '540.27', 'aut_centralizer_order': 24, 'aut_label': '45.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '15.a1.a1'], 'contains': ['90.b1.a1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8378, -1, 7400, -1, 7413, -1, 8074, -1], 'generators': [1, 2, 192], 'label': '540.27.45.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '45.b1.a1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120985
    {'ambient': '540.27', 'aut_centralizer_order': 24, 'aut_label': '45.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.b1', '15.a1.b1'], 'contains': ['90.b1.b1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8378, -1, 8510, -1, 7413, -1, 8843, -1], 'generators': [1, 2, 4], 'label': '540.27.45.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '45.b1.b1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120986
    {'ambient': '540.27', 'aut_centralizer_order': 24, 'aut_label': '45.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.c1', '15.a1.c1'], 'contains': ['90.b1.c1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8378, -1, 8871, -1, 7413, -1, 6681, -1], 'generators': [1, 2, 364], 'label': '540.27.45.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.c1', 'old_label': '45.b1.c1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120987
    {'ambient': '540.27', 'aut_centralizer_order': 24, 'aut_label': '45.b1', 'aut_quo_index': None, 'aut_stab_index': 60, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.d1', '15.a1.d1'], 'contains': ['90.b1.d1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8378, -1, 3308, -1, 7413, -1, 7385, -1], 'generators': [1, 2, 184], 'label': '540.27.45.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.d1', 'old_label': '45.b1.d1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.b1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120988
    {'ambient': '540.27', 'aut_centralizer_order': 4320, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4320, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.b1.a1', '18.b1.b1', '18.b1.c1', '18.b1.d1', '27.a1.a1'], 'contains': ['108.a1.a1', '270.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6324, 8502, 6244, 8747, 7149, 8710, 4225, 6324], 'generators': [2, 108], 'label': '540.27.54.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['108.a1.a1', '270.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '270.19', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120989
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.a1', 'complements': ['9.b1.b1', '9.b1.c1', '9.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'contains': ['180.a1.a1', '180.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2001, 3793, 1325, 3077, 3033, 4021, 2974, 3851], 'generators': [12, 360], 'label': '540.27.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'normal_contains': ['180.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120990
    {'ambient': '540.27', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 36, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.c1', '9.a1.a1', '9.b1.c1', '15.a1.c1'], 'core': '6.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [7517, -1, 8569, -1, 6336, -1, 5537, -1], 'generators': [1, 2, 364, 12, 108], 'label': '540.27.3.a1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '3.a1.c1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.c1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108120991
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.b1', 'complements': ['9.b1.a1', '9.b1.c1', '9.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.a1.a1', '30.a1.b1'], 'contains': ['180.a1.a1', '180.b1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2001, 3793, 1922, 3791, 3033, 4021, 3288, 4464], 'generators': [4, 12], 'label': '540.27.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': ['12.a1.b1', '20.a1.a1', '30.a1.b1'], 'normal_contains': ['180.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.b1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '60.a1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120992
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.c1', 'complements': ['9.b1.a1', '9.b1.d1', '9.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.c1', '20.a1.a1', '30.a1.c1'], 'contains': ['180.a1.a1', '180.b1.c1'], 'core': '60.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2001, 3793, 3544, 701, 3033, 4021, 1337, 5689], 'generators': [364, 12], 'label': '540.27.60.a1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.c1', 'normal_contained_in': ['12.a1.c1', '20.a1.a1', '30.a1.c1'], 'normal_contains': ['180.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.c1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '60.a1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120993
    {'ambient': '540.27', 'aut_centralizer_order': 360, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '6.a1.d1', 'complements': ['9.b1.a1', '9.b1.b1', '9.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.d1', '20.a1.a1', '30.a1.d1'], 'contains': ['180.a1.a1', '180.b1.d1'], 'core': '60.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2001, 3793, 576, 6854, 3033, 4021, 2324, 5077], 'generators': [184, 12], 'label': '540.27.60.a1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.d1', 'normal_contained_in': ['12.a1.d1', '20.a1.a1', '30.a1.d1'], 'normal_contains': ['180.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.d1', 'projective_image': '180.17', 'quotient_action_image': '6.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '60.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108120994
    {'ambient': '540.27', 'aut_centralizer_order': 8640, 'aut_label': '90.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.a1.a1', '30.a1.b1', '30.a1.c1', '30.a1.d1', '45.a1.a1'], 'contains': ['180.a1.a1', '270.a1.a1'], 'core': '90.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7035, 7098, 4992, 5615, 6336, 7203, 4531, 6922], 'generators': [2, 12], 'label': '540.27.90.a1.a1', 'mobius_quo': 1, 'mobius_sub': 135, 'normal_closure': '90.a1.a1', 'normal_contained_in': ['18.a1.a1', '30.a1.c1', '30.a1.b1', '30.a1.d1', '30.a1.a1'], 'normal_contains': ['180.a1.a1', '270.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '90.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '90.9', 'quotient_action_kernel_order': 90, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108120995
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.a1.a1', '45.b1.a1'], 'contains': ['180.b1.a1', '270.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5487, -1, 6166, -1, 5605, -1, 5082, -1], 'generators': [2, 360], 'label': '540.27.90.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '90.b1.a1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120996
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '30.a1.b1', '45.b1.b1'], 'contains': ['180.b1.b1', '270.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5487, -1, 6638, -1, 5605, -1, 5908, -1], 'generators': [2, 4], 'label': '540.27.90.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '90.b1.b1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120997
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.c1', '30.a1.c1', '45.b1.c1'], 'contains': ['180.b1.c1', '270.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5487, -1, 7144, -1, 5605, -1, 3919, -1], 'generators': [2, 364], 'label': '540.27.90.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '90.b1.c1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120998
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.d1', '30.a1.d1', '45.b1.d1'], 'contains': ['180.b1.d1', '270.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5487, -1, 2157, -1, 5605, -1, 4807, -1], 'generators': [2, 184], 'label': '540.27.90.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '30.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '90.b1.d1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108120999
    {'ambient': '540.27', 'aut_centralizer_order': 4320, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4320, 'centralizer': '2.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.b1.b1', '36.b1.c1', '36.b1.d1', '54.a1.a1'], 'contains': ['540.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3091, 7064, 3378, 8291, 5442, 7053, 2148, 4539], 'generators': [108], 'label': '540.27.108.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '54.a1.a1'], 'normal_contains': ['540.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '540.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.10', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108121000
    {'ambient': '540.27', 'aut_centralizer_order': 192, 'aut_label': '135.a1', 'aut_quo_index': None, 'aut_stab_index': 45, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '45.a1.a1', '45.b1.a1', '45.b1.b1', '45.b1.c1', '45.b1.d1'], 'contains': ['270.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [8171, -1, 8007, -1, 8145, -1, 7385, -1], 'generators': [1], 'label': '540.27.135.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '135.a1.a1', 'projective_image': '270.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '135.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108121001
    {'ambient': '540.27', 'aut_centralizer_order': 3, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '480.1197', 'aut_weyl_index': 36, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.d1', '9.a1.a1', '9.b1.d1', '15.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [7517, -1, 5510, -1, 6336, -1, 6280, -1], 'generators': [1, 2, 184, 12, 108], 'label': '540.27.3.a1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '3.a1.d1', 'projective_image': '90.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.d1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108121002
    {'ambient': '540.27', 'aut_centralizer_order': 8640, 'aut_label': '180.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.a1.a1', '60.a1.b1', '60.a1.c1', '60.a1.d1', '90.a1.a1'], 'contains': ['540.a1.a1'], 'core': '180.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3584, 5797, 1859, 5615, 4710, 5697, 2423, 5077], 'generators': [12], 'label': '540.27.180.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '180.a1.a1', 'normal_contained_in': ['36.a1.a1', '60.a1.c1', '60.a1.b1', '60.a1.d1', '60.a1.a1', '90.a1.a1'], 'normal_contains': ['540.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '180.17', 'quotient_action_image': '1.1', 'quotient_action_kernel': '180.17', 'quotient_action_kernel_order': 180, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108121003
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.a1.a1', '90.b1.a1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1806, -1, 2554, -1, 3938, -1, 2974, -1], 'generators': [360], 'label': '540.27.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '180.b1.a1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108121004
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.b1', '60.a1.b1', '90.b1.b1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1806, -1, 4066, -1, 3938, -1, 3449, -1], 'generators': [4], 'label': '540.27.180.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '180.b1.b1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108121005
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.c1', '60.a1.c1', '90.b1.c1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1806, -1, 4953, -1, 3938, -1, 1605, -1], 'generators': [364], 'label': '540.27.180.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '180.b1.c1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108121006
    {'ambient': '540.27', 'aut_centralizer_order': 720, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '6.a1.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.d1', '60.a1.d1', '90.b1.d1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1806, -1, 728, -1, 3938, -1, 2699, -1], 'generators': [184], 'label': '540.27.180.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '180.b1.d1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 108121007
    {'ambient': '540.27', 'aut_centralizer_order': 17280, 'aut_label': '270.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 17280, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '90.a1.a1', '90.b1.a1', '90.b1.b1', '90.b1.c1', '90.b1.d1', '135.a1.a1'], 'contains': ['540.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6360, 8005, 6272, 7439, 6336, 8409, 4669, 6324], 'generators': [2], 'label': '540.27.270.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '270.a1.a1', 'normal_contained_in': ['54.a1.a1', '90.a1.a1'], 'normal_contains': ['540.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '270.a1.a1', 'projective_image': '270.19', 'quotient_action_image': '1.1', 'quotient_action_kernel': '270.19', 'quotient_action_kernel_order': 270, 'quotient_fusion': None, 'short_label': '270.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108121008
    {'ambient': '540.27', 'aut_centralizer_order': None, 'aut_label': '540.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '180.a1.a1', '180.b1.a1', '180.b1.b1', '180.b1.c1', '180.b1.d1', '270.a1.a1'], 'contains': [], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2609, 7064, 3378, 7439, 5076, 7053, 2699, 5077], 'generators': [], 'label': '540.27.540.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '540.a1.a1', 'normal_contained_in': ['108.a1.a1', '180.a1.a1', '270.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '540.a1.a1', 'projective_image': '540.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '540.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108121009
    {'ambient': '540.27', 'aut_centralizer_order': 10, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.46191', 'aut_weyl_index': 10, 'centralizer': '18.a1.a1', 'complements': ['135.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1', '12.a1.b1', '12.a1.c1', '12.a1.d1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1003, 1498, 979, 5124, 889, 1648, 1417, 2066], 'generators': [4, 108, 12, 360], 'label': '540.27.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.c1', '12.a1.b1', '12.a1.d1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '180.17', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108121011
    {'ambient': '540.27', 'aut_centralizer_order': 90, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '48.35', 'aut_weyl_index': 360, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '18.b1.a1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4479, 5797, 4321, 4187, 4659, 8635, 3345, 3396], 'generators': [2, 360, 108, 12], 'label': '540.27.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '90.9', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}