Abstract group data - 540.76

Formats: - HTML - YAML - JSON - 2025-09-24T09:01:20.189691

• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [2, 6, 2, 4, 6, 6, 5], 'aut_gens': [[1, 2, 6, 18], [1, 2, 12, 522], [193, 8, 6, 342], [271, 2, 6, 342], [1, 2, 6, 234], [5, 2, 6, 348], [1, 366, 6, 524], [109, 2, 6, 18]], 'aut_group': '17280.fp', 'aut_hash': 7336759155281172877, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17280, 'aut_permdeg': 90, 'aut_perms': [13357779239927666839809778456543992889412518401823662532893362271125824152719785631360555617509030751232945427097292785657760765676608309, 978613680725323270384434294457193026921394144055421984018444271912762099360789422859598132352700472478959216594635672207122762056079380869, 279004299646206441845458296556284371251574540062133696495377982428251485111916975396247019002808891086425910916239835508541725453593359823, 16139122172685439329720083305288619421418590216798701673118038559552406498722208608113309694749490966560804142448254012500870040737823139, 75863757752509316609258673884453135207185806119270676776384000385981663829215367589309020766472407799566776833970477494832762008179991989, 13702594761328959788500468831365115559273828929113376101760182677903942625737987505725434495002562825267124380807410410050676090151522869, 98130979101455530525240081550282725754448652195002864852508550686779444130136165331085921397085458917280086494666833177277615687252260217], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 45, 2, 1], [3, 1, 2, 1], [3, 6, 4, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 6, 4, 1], [6, 45, 4, 1], [10, 2, 2, 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], [2, 45, 2], [3, 1, 2], [3, 6, 4], [5, 2, 2], [6, 1, 2], [6, 6, 4], [6, 45, 4], [10, 2, 2], [15, 2, 4], [15, 6, 16], [30, 2, 4], [30, 6, 16]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, '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': 76, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['270.19', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 45, 1, 2], [3, 1, 2, 1], [3, 6, 1, 4], [5, 2, 2, 1], [6, 1, 2, 1], [6, 6, 1, 4], [6, 45, 2, 2], [10, 2, 2, 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': 3402, 'exponent': 30, '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': '3.1', 'frattini_quotient': '180.36', 'hash': 76, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 3, 1, 15], 'inner_gens': [[1, 4, 6, 534], [5, 2, 6, 24], [1, 2, 6, 18], [43, 14, 6, 18]], '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': '540.76', 'linC_count': 216, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 6, 'linQ_dim': 10, 'linQ_dim_count': 6, 'linR_count': 108, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:D30', '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': 28, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 110, 'number_subgroups': 850, 'old_label': None, 'order': 540, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 91], [3, 26], [5, 4], [6, 206], [10, 4], [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, 12, 20], [271, 192, 6, 208], [1, 364, 6, 28], [1, 188, 6, 416], [1, 192, 6, 388]], 'outer_group': '192.1480', 'outer_hash': 1480, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 18, 'outer_perms': [11913376991400, 1166514173052841, 2297134228929240, 4764534621827160, 2657282294944104], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3):C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 2], [6, 4], [8, 8], [24, 2]], 'representations': {'PC': {'code': 3453579399119156924909981761863, 'gens': [1, 2, 3, 4], 'pres': [6, 2, 3, 3, 2, 3, 5, 49, 12819, 297, 69, 15304, 730, 118, 15557]}, 'Perm': {'d': 16, 'gens': [287411886847, 1, 1601792277120, 2815618619520, 966, 4292504254080]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:D_{30}', 'transitive_degree': 90, '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: 138647154
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 76, 'group_order': 540, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 138647165
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 76, 'group_order': 540, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 270, 'size': 1}
  • id: 138647176
    {'aut_label': '2B', 'centralizer': '45.a1.a1', 'counter': 3, 'group_counter': 76, 'group_order': 540, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 31, 'size': 45}
  • id: 138647187
    {'aut_label': '2B', 'centralizer': '45.a1.a1', 'counter': 4, 'group_counter': 76, 'group_order': 540, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 109, 'size': 45}
  • id: 138647198
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 76, 'group_order': 540, 'label': '3A1', 'order': 3, 'powers': [6, 1, 6], 'representative': 6, 'size': 1}
  • id: 138647209
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 76, 'group_order': 540, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 5], 'representative': 12, 'size': 1}
  • id: 138647215
    {'aut_label': '3B', 'centralizer': '6.a1.a1', 'counter': 7, 'group_counter': 76, 'group_order': 540, 'label': '3B', 'order': 3, 'powers': [7, 1, 7], 'representative': 180, 'size': 6}
  • id: 138647216
    {'aut_label': '3B', 'centralizer': '6.a1.b1', 'counter': 8, 'group_counter': 76, 'group_order': 540, 'label': '3C', 'order': 3, 'powers': [8, 1, 8], 'representative': 182, 'size': 6}
  • id: 138647217
    {'aut_label': '3B', 'centralizer': '6.a1.c1', 'counter': 9, 'group_counter': 76, 'group_order': 540, 'label': '3D', 'order': 3, 'powers': [9, 1, 9], 'representative': 184, 'size': 6}
  • id: 138647155
    {'aut_label': '3B', 'centralizer': '6.a1.d1', 'counter': 10, 'group_counter': 76, 'group_order': 540, 'label': '3E', 'order': 3, 'powers': [10, 1, 10], 'representative': 2, 'size': 6}
  • id: 138647156
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 76, 'group_order': 540, 'label': '5A1', 'order': 5, 'powers': [12, 12, 1], 'representative': 324, 'size': 2}
  • id: 138647157
    {'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 76, 'group_order': 540, 'label': '5A2', 'order': 5, 'powers': [11, 11, 1], 'representative': 108, 'size': 2}
  • id: 138647158
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 76, 'group_order': 540, 'label': '6A1', 'order': 6, 'powers': [5, 2, 14], 'representative': 282, 'size': 1}
  • id: 138647159
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 76, 'group_order': 540, 'label': '6A-1', 'order': 6, 'powers': [6, 2, 13], 'representative': 276, 'size': 1}
  • id: 138647160
    {'aut_label': '6B', 'centralizer': '6.a1.a1', 'counter': 15, 'group_counter': 76, 'group_order': 540, 'label': '6B', 'order': 6, 'powers': [7, 2, 15], 'representative': 90, 'size': 6}
  • id: 138647161
    {'aut_label': '6B', 'centralizer': '6.a1.b1', 'counter': 16, 'group_counter': 76, 'group_order': 540, 'label': '6C', 'order': 6, 'powers': [8, 2, 16], 'representative': 100, 'size': 6}
  • id: 138647162
    {'aut_label': '6B', 'centralizer': '6.a1.c1', 'counter': 17, 'group_counter': 76, 'group_order': 540, 'label': '6D', 'order': 6, 'powers': [9, 2, 17], 'representative': 104, 'size': 6}
  • id: 138647163
    {'aut_label': '6B', 'centralizer': '6.a1.d1', 'counter': 18, 'group_counter': 76, 'group_order': 540, 'label': '6E', 'order': 6, 'powers': [10, 2, 18], 'representative': 274, 'size': 6}
  • id: 138647164
    {'aut_label': '6F1', 'centralizer': '45.a1.a1', 'counter': 19, 'group_counter': 76, 'group_order': 540, 'label': '6F1', 'order': 6, 'powers': [5, 3, 20], 'representative': 25, 'size': 45}
  • id: 138647166
    {'aut_label': '6F1', 'centralizer': '45.a1.a1', 'counter': 20, 'group_counter': 76, 'group_order': 540, 'label': '6F-1', 'order': 6, 'powers': [6, 3, 19], 'representative': 19, 'size': 45}
  • id: 138647167
    {'aut_label': '6F1', 'centralizer': '45.a1.a1', 'counter': 21, 'group_counter': 76, 'group_order': 540, 'label': '6G1', 'order': 6, 'powers': [6, 4, 22], 'representative': 115, 'size': 45}
  • id: 138647168
    {'aut_label': '6F1', 'centralizer': '45.a1.a1', 'counter': 22, 'group_counter': 76, 'group_order': 540, 'label': '6G-1', 'order': 6, 'powers': [5, 4, 21], 'representative': 121, 'size': 45}
  • id: 138647169
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 23, 'group_counter': 76, 'group_order': 540, 'label': '10A1', 'order': 10, 'powers': [11, 24, 2], 'representative': 162, 'size': 2}
  • id: 138647170
    {'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 24, 'group_counter': 76, 'group_order': 540, 'label': '10A3', 'order': 10, 'powers': [12, 23, 2], 'representative': 486, 'size': 2}
  • id: 138647171
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 25, 'group_counter': 76, 'group_order': 540, 'label': '15A1', 'order': 15, 'powers': [27, 11, 5], 'representative': 120, 'size': 2}
  • id: 138647172
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 76, 'group_order': 540, 'label': '15A-1', 'order': 15, 'powers': [28, 11, 6], 'representative': 438, 'size': 2}
  • id: 138647173
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 76, 'group_order': 540, 'label': '15A2', 'order': 15, 'powers': [25, 12, 6], 'representative': 222, 'size': 2}
  • id: 138647174
    {'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 76, 'group_order': 540, 'label': '15A-2', 'order': 15, 'powers': [26, 12, 5], 'representative': 336, 'size': 2}
  • id: 138647175
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 29, 'group_counter': 76, 'group_order': 540, 'label': '15B1', 'order': 15, 'powers': [30, 12, 7], 'representative': 36, 'size': 6}
  • id: 138647177
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 30, 'group_counter': 76, 'group_order': 540, 'label': '15B2', 'order': 15, 'powers': [31, 11, 7], 'representative': 72, 'size': 6}
  • id: 138647178
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 31, 'group_counter': 76, 'group_order': 540, 'label': '15B4', 'order': 15, 'powers': [32, 12, 7], 'representative': 144, 'size': 6}
  • id: 138647179
    {'aut_label': '15B1', 'centralizer': '6.a1.a1', 'counter': 32, 'group_counter': 76, 'group_order': 540, 'label': '15B7', 'order': 15, 'powers': [29, 11, 7], 'representative': 252, 'size': 6}
  • id: 138647180
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 33, 'group_counter': 76, 'group_order': 540, 'label': '15C1', 'order': 15, 'powers': [34, 12, 8], 'representative': 46, 'size': 6}
  • id: 138647181
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 34, 'group_counter': 76, 'group_order': 540, 'label': '15C2', 'order': 15, 'powers': [35, 11, 8], 'representative': 74, 'size': 6}
  • id: 138647182
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 35, 'group_counter': 76, 'group_order': 540, 'label': '15C4', 'order': 15, 'powers': [36, 12, 8], 'representative': 154, 'size': 6}
  • id: 138647183
    {'aut_label': '15B1', 'centralizer': '6.a1.b1', 'counter': 36, 'group_counter': 76, 'group_order': 540, 'label': '15C7', 'order': 15, 'powers': [33, 11, 8], 'representative': 262, 'size': 6}
  • id: 138647184
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 37, 'group_counter': 76, 'group_order': 540, 'label': '15D1', 'order': 15, 'powers': [38, 12, 9], 'representative': 50, 'size': 6}
  • id: 138647185
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 38, 'group_counter': 76, 'group_order': 540, 'label': '15D2', 'order': 15, 'powers': [39, 11, 9], 'representative': 76, 'size': 6}
  • id: 138647186
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 39, 'group_counter': 76, 'group_order': 540, 'label': '15D4', 'order': 15, 'powers': [40, 12, 9], 'representative': 158, 'size': 6}
  • id: 138647188
    {'aut_label': '15B1', 'centralizer': '6.a1.c1', 'counter': 40, 'group_counter': 76, 'group_order': 540, 'label': '15D7', 'order': 15, 'powers': [37, 11, 9], 'representative': 266, 'size': 6}
  • id: 138647189
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 41, 'group_counter': 76, 'group_order': 540, 'label': '15E1', 'order': 15, 'powers': [42, 11, 10], 'representative': 112, 'size': 6}
  • id: 138647190
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 42, 'group_counter': 76, 'group_order': 540, 'label': '15E2', 'order': 15, 'powers': [43, 12, 10], 'representative': 218, 'size': 6}
  • id: 138647191
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 43, 'group_counter': 76, 'group_order': 540, 'label': '15E4', 'order': 15, 'powers': [44, 11, 10], 'representative': 436, 'size': 6}
  • id: 138647192
    {'aut_label': '15B1', 'centralizer': '6.a1.d1', 'counter': 44, 'group_counter': 76, 'group_order': 540, 'label': '15E7', 'order': 15, 'powers': [41, 12, 10], 'representative': 220, 'size': 6}
  • id: 138647193
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 45, 'group_counter': 76, 'group_order': 540, 'label': '30A1', 'order': 30, 'powers': [25, 23, 13], 'representative': 60, 'size': 2}
  • id: 138647194
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 46, 'group_counter': 76, 'group_order': 540, 'label': '30A-1', 'order': 30, 'powers': [26, 23, 14], 'representative': 66, 'size': 2}
  • id: 138647195
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 47, 'group_counter': 76, 'group_order': 540, 'label': '30A7', 'order': 30, 'powers': [28, 24, 13], 'representative': 168, 'size': 2}
  • id: 138647196
    {'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 48, 'group_counter': 76, 'group_order': 540, 'label': '30A-7', 'order': 30, 'powers': [27, 24, 14], 'representative': 174, 'size': 2}
  • id: 138647197
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 49, 'group_counter': 76, 'group_order': 540, 'label': '30B1', 'order': 30, 'powers': [29, 24, 15], 'representative': 18, 'size': 6}
  • id: 138647199
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 50, 'group_counter': 76, 'group_order': 540, 'label': '30B7', 'order': 30, 'powers': [32, 23, 15], 'representative': 126, 'size': 6}
  • id: 138647200
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 51, 'group_counter': 76, 'group_order': 540, 'label': '30B11', 'order': 30, 'powers': [31, 24, 15], 'representative': 342, 'size': 6}
  • id: 138647201
    {'aut_label': '30B1', 'centralizer': '6.a1.a1', 'counter': 52, 'group_counter': 76, 'group_order': 540, 'label': '30B13', 'order': 30, 'powers': [30, 23, 15], 'representative': 234, 'size': 6}
  • id: 138647202
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 53, 'group_counter': 76, 'group_order': 540, 'label': '30C1', 'order': 30, 'powers': [33, 24, 16], 'representative': 20, 'size': 6}
  • id: 138647203
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 54, 'group_counter': 76, 'group_order': 540, 'label': '30C7', 'order': 30, 'powers': [36, 23, 16], 'representative': 128, 'size': 6}
  • id: 138647204
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 55, 'group_counter': 76, 'group_order': 540, 'label': '30C11', 'order': 30, 'powers': [35, 24, 16], 'representative': 344, 'size': 6}
  • id: 138647205
    {'aut_label': '30B1', 'centralizer': '6.a1.b1', 'counter': 56, 'group_counter': 76, 'group_order': 540, 'label': '30C13', 'order': 30, 'powers': [34, 23, 16], 'representative': 236, 'size': 6}
  • id: 138647206
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 57, 'group_counter': 76, 'group_order': 540, 'label': '30D1', 'order': 30, 'powers': [37, 24, 17], 'representative': 22, 'size': 6}
  • id: 138647207
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 58, 'group_counter': 76, 'group_order': 540, 'label': '30D7', 'order': 30, 'powers': [40, 23, 17], 'representative': 130, 'size': 6}
  • id: 138647208
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 59, 'group_counter': 76, 'group_order': 540, 'label': '30D11', 'order': 30, 'powers': [39, 24, 17], 'representative': 346, 'size': 6}
  • id: 138647210
    {'aut_label': '30B1', 'centralizer': '6.a1.c1', 'counter': 60, 'group_counter': 76, 'group_order': 540, 'label': '30D13', 'order': 30, 'powers': [38, 23, 17], 'representative': 238, 'size': 6}
  • id: 138647211
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 61, 'group_counter': 76, 'group_order': 540, 'label': '30E1', 'order': 30, 'powers': [41, 23, 18], 'representative': 56, 'size': 6}
  • id: 138647212
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 62, 'group_counter': 76, 'group_order': 540, 'label': '30E7', 'order': 30, 'powers': [44, 24, 18], 'representative': 166, 'size': 6}
  • id: 138647213
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 63, 'group_counter': 76, 'group_order': 540, 'label': '30E11', 'order': 30, 'powers': [43, 23, 18], 'representative': 58, 'size': 6}
  • id: 138647214
    {'aut_label': '30B1', 'centralizer': '6.a1.d1', 'counter': 64, 'group_counter': 76, 'group_order': 540, 'label': '30E13', 'order': 30, 'powers': [42, 24, 18], 'representative': 164, '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: 12293031
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.1a', '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: 12293042
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.1b', '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: 12293052
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12293053
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12293054
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1], 'schur_index': 1}
  • id: 12293055
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -1, -1, 2, -1, 2, 2, 2, 2, -1, -1, -1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2], 'schur_index': 1}
  • id: 12293056
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, 2, 2, -1, 2, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12293057
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
  • id: 12293058
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, -1, -1, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1], 'schur_index': 1}
  • id: 12293032
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, -1, -1, 2, -1, 2, 2, -2, -2, 1, 1, 1, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2], 'schur_index': 1}
  • id: 12293033
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, -1, 2, -1, -1, 2, 2, -2, -2, 1, -2, 1, 1, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -2, -2, -2, -2, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12293034
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12293035
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2i', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, 4, 4, -1, -1, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12293036
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2j', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, -1, -1, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12293046
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.3a', 'multiplicity': 2, 'nt': [9, 12], 'qdim': 6, 'qvalues': [6, 6, 2, 2, -3, -3, 0, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, -1, -1, -1, -1, 6, 6, -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: 12293047
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.3b', 'multiplicity': 2, 'nt': [18, 24], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -3, -3, 0, 0, 0, 0, 6, 6, -3, -3, 0, 0, 0, 0, 1, 1, 1, 1, 6, 6, -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: 12293048
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.3c', 'multiplicity': 2, 'nt': [18, 52], 'qdim': 6, 'qvalues': [6, -6, -2, 2, -3, -3, 0, 0, 0, 0, 6, 6, 3, 3, 0, 0, 0, 0, 1, 1, -1, -1, -6, -6, -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: 12293049
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.3d', 'multiplicity': 2, 'nt': [18, 52], 'qdim': 6, 'qvalues': [6, -6, 2, -2, -3, -3, 0, 0, 0, 0, 6, 6, 3, 3, 0, 0, 0, 0, -1, -1, 1, 1, -6, -6, -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: 12293037
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2k', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, -4, -4, -4, 8, -2, -2, 8, 8, 8, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, -2, 1, 1, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 1, 1], 'schur_index': 1}
  • id: 12293038
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2l', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, -4, -4, 8, -4, -2, -2, 8, 8, -4, -4, -4, 8, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2], 'schur_index': 1}
  • id: 12293039
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2m', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, -4, 8, -4, -4, -2, -2, 8, 8, -4, 8, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12293040
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2n', 'multiplicity': 4, 'nt': [15, 2], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, 8, -4, -4, -4, -2, -2, 8, 8, -4, -4, 8, -4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
  • id: 12293041
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2o', 'multiplicity': 4, 'nt': [30, 14], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, -4, -4, -4, 8, -2, -2, -8, -8, -8, 4, 4, 4, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, -2, 1, 1, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1], 'schur_index': 1}
  • id: 12293043
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2p', 'multiplicity': 4, 'nt': [30, 14], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, -4, -4, 8, -4, -2, -2, -8, -8, 4, 4, 4, -8, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2], 'schur_index': 1}
  • id: 12293044
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2q', 'multiplicity': 4, 'nt': [30, 14], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, -4, 8, -4, -4, -2, -2, -8, -8, 4, -8, 4, 4, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 2, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12293045
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.2r', 'multiplicity': 4, 'nt': [30, 14], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, 8, -4, -4, -4, -2, -2, -8, -8, 4, 4, -8, 4, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
  • id: 12293050
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.6a', 'multiplicity': 4, 'nt': [45, 31], 'qdim': 24, 'qvalues': [24, 24, 0, 0, -12, -12, 0, 0, 0, 0, -6, -6, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 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: 12293051
    {'cdim': 6, 'counter': 28, 'faithful': True, 'group': '540.76', 'group_order': 540, 'image': None, 'label': '540.76.6b', 'multiplicity': 4, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, -12, -12, 0, 0, 0, 0, -6, -6, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 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: 28522114
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 540, 'label': '540.76.1a', '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: 28522125
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 270, 'label': '540.76.1b', '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: 28522136
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 270, 'label': '540.76.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 28522147
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 540, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 270, 'label': '540.76.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 28522158
    {'center': '6.a1.d1', 'center_index': 6, 'center_order': 90, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.d1', 'kernel_order': 90, 'label': '540.76.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 28522169
    {'center': '6.a1.c1', 'center_index': 6, 'center_order': 90, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.c1', 'kernel_order': 90, 'label': '540.76.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
  • id: 28522175
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 90, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.b1', 'kernel_order': 90, 'label': '540.76.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 28522176
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 90, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 90, 'label': '540.76.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
  • id: 28522177
    {'center': '6.a1.d1', 'center_index': 6, 'center_order': 90, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.d1', 'kernel_order': 45, 'label': '540.76.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
  • id: 28522115
    {'center': '6.a1.c1', 'center_index': 6, 'center_order': 90, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.c1', 'kernel_order': 45, 'label': '540.76.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 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]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]]]}
  • id: 28522116
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 90, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.b1', 'kernel_order': 45, 'label': '540.76.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 28522117
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 90, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 45, 'label': '540.76.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]]]}
  • id: 28522118
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 13, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 54, 'label': '540.76.2i1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 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]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 28522119
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 14, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 54, 'label': '540.76.2i2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[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, 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]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 28522120
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 15, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 27, 'label': '540.76.2j1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 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]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 28522121
    {'center': '10.a1.a1', 'center_index': 10, 'center_order': 54, 'counter': 16, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 27, 'label': '540.76.2j2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[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, 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]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 28522122
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 17, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.76.2k1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[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, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[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, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[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]]]}
  • id: 28522123
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 18, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.76.2k2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[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, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[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, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[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, 4], [1, -4]]]}
  • id: 28522124
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 19, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.76.2k3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[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, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[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, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[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]]]}
  • id: 28522126
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 20, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.d1', 'kernel_order': 18, 'label': '540.76.2k4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[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, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[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, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[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]]]}
  • id: 28522127
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 21, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.76.2l1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[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, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 6], [1, -6]]]}
  • id: 28522128
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 22, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.76.2l2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[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, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 6], [1, -6]]]}
  • id: 28522129
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 23, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.76.2l3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[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, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[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, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 3], [1, -3]]]}
  • id: 28522130
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 24, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.c1', 'kernel_order': 18, 'label': '540.76.2l4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[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, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[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, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
  • id: 28522131
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 25, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.76.2m1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[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, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]]]}
  • id: 28522132
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 26, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.76.2m2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[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, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]]]}
  • id: 28522133
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 27, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.76.2m3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[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, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 7], [1, -7]]]}
  • id: 28522134
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 28, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.b1', 'kernel_order': 18, 'label': '540.76.2m4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[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, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[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, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]]]}
  • id: 28522135
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 29, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.76.2n1', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 1], [1, -1]]]}
  • id: 28522137
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 30, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.76.2n2', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 4], [1, -4]]]}
  • id: 28522138
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 31, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.76.2n3', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 7], [1, -7]]]}
  • id: 28522139
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 32, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '30.3', 'image_order': 30, 'indicator': 1, 'kernel': '30.a1.a1', 'kernel_order': 18, 'label': '540.76.2n4', 'nt': [15, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
  • id: 28522140
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 33, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.d1', 'kernel_order': 9, 'label': '540.76.2o1', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-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, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[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, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-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]]]}
  • id: 28522141
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 34, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.d1', 'kernel_order': 9, 'label': '540.76.2o2', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-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, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[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, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-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, 4], [-1, -4]]]}
  • id: 28522142
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 35, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.d1', 'kernel_order': 9, 'label': '540.76.2o3', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-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, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[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, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-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]]]}
  • id: 28522143
    {'center': '30.a1.d1', 'center_index': 30, 'center_order': 18, 'counter': 36, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.d1', 'kernel_order': 9, 'label': '540.76.2o4', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-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, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[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, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-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]]]}
  • id: 28522144
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 37, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.c1', 'kernel_order': 9, 'label': '540.76.2p1', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-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, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[-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, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]]]}
  • id: 28522145
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 38, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.c1', 'kernel_order': 9, 'label': '540.76.2p2', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-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, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-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, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]]]}
  • id: 28522146
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 39, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.c1', 'kernel_order': 9, 'label': '540.76.2p3', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-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, 6], [1, -6]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[-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, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]]]}
  • id: 28522148
    {'center': '30.a1.c1', 'center_index': 30, 'center_order': 18, 'counter': 40, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.c1', 'kernel_order': 9, 'label': '540.76.2p4', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-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, 6], [1, -6]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-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, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
  • id: 28522149
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 41, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 9, 'label': '540.76.2q1', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-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, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[-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, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]]]}
  • id: 28522150
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 42, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 9, 'label': '540.76.2q2', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-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, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-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, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 28522151
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 43, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 9, 'label': '540.76.2q3', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-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, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-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, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]]]}
  • id: 28522152
    {'center': '30.a1.b1', 'center_index': 30, 'center_order': 18, 'counter': 44, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.b1', 'kernel_order': 9, 'label': '540.76.2q4', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-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, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-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, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]]]}
  • id: 28522153
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 45, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 9, 'label': '540.76.2r1', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]]]}
  • id: 28522154
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 46, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 9, 'label': '540.76.2r2', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]]]}
  • id: 28522155
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 47, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 9, 'label': '540.76.2r3', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]]]}
  • id: 28522156
    {'center': '30.a1.a1', 'center_index': 30, 'center_order': 18, 'counter': 48, 'cyclotomic_n': 15, 'dim': 2, 'faithful': False, 'field': [1, 4, -4, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '60.12', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 9, 'label': '540.76.2r4', 'nt': [30, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]]]}
  • id: 28522157
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 49, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 10, 'label': '540.76.3a1', 'nt': [9, 12], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[3, 0]], [[3, 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]], [[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: 28522159
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 50, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 10, 'label': '540.76.3a2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[3, 0]], [[3, 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]], [[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: 28522160
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 51, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 10, 'label': '540.76.3b1', 'nt': [18, 24], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[3, 0]], [[3, 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]], [[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: 28522161
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 52, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '54.8', 'image_order': 54, 'indicator': 0, 'kernel': '54.a1.a1', 'kernel_order': 10, 'label': '540.76.3b2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[3, 0]], [[3, 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]], [[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: 28522162
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 53, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '108.28', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.76.3c1', 'nt': [18, 52], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-3, 0]], [[-3, 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]], [[-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: 28522163
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 54, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '108.28', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.76.3c2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-3, 0]], [[-3, 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]], [[-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: 28522164
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 55, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '108.28', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.76.3d1', 'nt': [18, 52], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-3, 0]], [[-3, 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]], [[-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: 28522165
    {'center': '18.a1.a1', 'center_index': 18, 'center_order': 30, 'counter': 56, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '108.28', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 5, 'label': '540.76.3d2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-3, 0]], [[-3, 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]], [[-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: 28522166
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.76.6a1', 'nt': [45, 31], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, -5]], [[6, 5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[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]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 28522167
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.76.6a2', 'nt': [45, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 5]], [[6, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 3], [3, -3]], [[3, 6], [3, -6]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[-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, 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, 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]], [[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: 28522168
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.76.6a3', 'nt': [45, 31], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, -5]], [[6, 5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 1], [3, 4]], [[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]], [[-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]], [[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: 28522170
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '270.19', 'image_order': 270, 'indicator': 0, 'kernel': '270.a1.a1', 'kernel_order': 2, 'label': '540.76.6a4', 'nt': [45, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 5]], [[6, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6], [3, -6]], [[3, 3], [3, -3]], [[3, 1], [3, 4]], [[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, 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, 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]], [[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: 28522171
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '540.76', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.76.6b1', 'nt': [90, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, -5]], [[6, 5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 3], [-3, -3]], [[-3, 6], [-3, -6]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [-3, 5], [3, 7]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[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]], [[-3, 0], [3, 1], [3, 2], [-3, 3], [3, 4], [3, 7]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 28522172
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '540.76', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.76.6b2', 'nt': [90, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 5]], [[6, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 3], [-3, -3]], [[-3, 6], [-3, -6]], [[3, 0], [-3, 1], [-3, 4], [3, 5]], [[-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, 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, 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]], [[-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: 28522173
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '540.76', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.76.6b3', 'nt': [90, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, -5]], [[6, 5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6], [-3, -6]], [[-3, 3], [-3, -3]], [[3, 0], [-3, 1], [-3, 2], [3, 3], [-3, 4], [-3, 7]], [[3, 1], [3, 4]], [[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]], [[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]], [[-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: 28522174
    {'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': '540.76', 'group_counter': 76, 'group_order': 540, 'image': None, 'image_isoclass': '540.76', 'image_order': 540, 'indicator': 0, 'kernel': '540.a1.a1', 'kernel_order': 1, 'label': '540.76.6b4', 'nt': [90, 4], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 5]], [[6, -5]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6], [-3, -6]], [[-3, 3], [-3, -3]], [[3, 1], [3, 4]], [[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, 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, 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]], [[-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: 108124254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 540, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '540.76.1.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': '540.76', 'subgroup_hash': 76, 'subgroup_order': 540, 'subgroup_tex': 'C_3^2:D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 270, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.2.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'], 'split': True, '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: 108124287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 270, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '540.76.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '270.19', 'subgroup_hash': 19, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 270, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '540.76.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '270.19', 'subgroup_hash': 19, 'subgroup_order': 270, 'subgroup_tex': 'C_3^2:D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124309
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '180.34', 'subgroup_hash': 34, 'subgroup_order': 180, 'subgroup_tex': 'C_3\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124320
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.3.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '180.34', 'subgroup_hash': 34, 'subgroup_order': 180, 'subgroup_tex': 'C_3\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.3.a1.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '180.34', 'subgroup_hash': 34, 'subgroup_order': 180, 'subgroup_tex': 'C_3\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 90, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.3.a1.d1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '180.34', 'subgroup_hash': 34, 'subgroup_order': 180, 'subgroup_tex': 'C_3\\times D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 135, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 15, 'label': '540.76.4.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': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['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: 108124255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '540.76.5.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': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 108124266
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.6.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': True, '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: 108124268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.6.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': True, '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: 108124269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.6.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': True, '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: 108124270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 90, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.6.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': True, '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: 108124271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124275
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 45, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.6.b1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 30, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 108124281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.9.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.9.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.9.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 108124285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 54, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.10.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': True, '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: 108124286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.12.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': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 108124290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.12.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': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 108124291
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.12.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': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 108124292
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 45, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.12.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': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['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: 108124293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.15.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.15.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.15.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124297
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 30, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.76.18.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: 108124299
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.18.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: 108124300
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.18.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: 108124301
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.18.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: 108124302
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 10, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.18.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: 108124303
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 108124304
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 108124305
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124306
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124307
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124308
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124310
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124311
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124312
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124313
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.18.d1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 108124314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 27, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '540.76.20.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': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', '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: 108124315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 10, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '540.76.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 108124316
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.30.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': True, '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: 108124317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.30.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': True, '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: 108124318
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.30.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': True, '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: 108124319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 18, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.30.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': True, '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: 108124321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.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': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.30.b1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124329
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 15, 'counter': 68, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.76.36.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': '36.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3', '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: 108124330
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.36.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: 108124332
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.36.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: 108124333
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.36.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: 108124334
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 5, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.36.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: 108124335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.45.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 108124336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.45.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 108124337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.45.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 108124338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.45.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 108124339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.45.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 108124340
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 10, 'counter': 78, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.76.54.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 108124341
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 108124343
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.54.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 108124344
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.60.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': '60.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{30}', '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: 108124345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.60.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': '60.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{30}', '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: 108124346
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.60.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': '60.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{30}', '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: 108124347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 9, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '540.76.60.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': '60.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{30}', '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: 108124348
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 6, 'counter': 85, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.76.90.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', '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: 108124349
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.90.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: 108124350
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.90.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: 108124351
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.90.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: 108124352
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.90.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: 108124354
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 108124355
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.90.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '90.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 108124356
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124357
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124358
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124359
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124360
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124361
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124362
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124363
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '540.76.90.d1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 108124256
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 270, 'characteristic': True, 'core_order': 5, 'counter': 100, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '540.76.108.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': '108.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': True, 'solvable': True, 'special_labels': [], '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: 108124257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '540.76.135.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 108124258
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 3, 'counter': 102, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '540.76.180.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': '180.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 180, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{30}', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'D2', 'C5'], '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: 108124259
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.180.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: 108124260
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.180.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: 108124261
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.180.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: 108124262
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 90, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.180.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: 108124263
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 2, 'counter': 107, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '540.76.270.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 108124264
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.270.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 108124265
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '540.76.270.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '270.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': 270, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 108124267
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '540.76', 'ambient_counter': 76, 'ambient_order': 540, 'ambient_tex': 'C_3^2:D_{30}', 'central': True, 'central_factor': False, 'centralizer_order': 540, 'characteristic': True, 'core_order': 1, 'counter': 110, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '540.76.540.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': '540.76', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 76, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 540, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_{30}', '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: 108124254
    {'ambient': '540.76', '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', '2.b1.a1', '2.b1.b1', '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': [1986, 6793, 5643, 5853, 4176, 3642, 5545, 3306], 'generators': [1, 6, 2, 366, 270, 108], 'label': '540.76.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], '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: 108124255
    {'ambient': '540.76', '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', '10.b1.a1', '10.b1.b1', '15.a1.a1', '15.a1.b1', '15.a1.c1', '15.a1.d1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1350, -1, 5729, -1, 3432, -1, 6873, -1], 'generators': [1, 6, 270, 2, 366], 'label': '540.76.5.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: 108124256
    {'ambient': '540.76', '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', '54.b1.a1', '54.b1.b1'], 'contains': ['540.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6963, 538, 4715, 8417, 7304, 7128, 3642, 4539], 'generators': [108], 'label': '540.76.108.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': '540.76', '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: 108124257
    {'ambient': '540.76', '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', '270.b1.a1', '270.b1.b1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7563, -1, 7549, -1, 8693, -1, 3901, -1], 'generators': [1, 270], 'label': '540.76.135.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: 108124258
    {'ambient': '540.76', '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', '90.c1.a1', '90.c1.b1'], 'contains': ['540.a1.a1'], 'core': '180.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5588, 4901, 3441, 5398, 5035, 5807, 4669, 5077], 'generators': [6], 'label': '540.76.180.a1.a1', 'mobius_quo': -1, 'mobius_sub': -270, 'normal_closure': '180.a1.a1', 'normal_contained_in': ['36.a1.a1', '60.a1.c1', '60.a1.a1', '60.a1.b1', '60.a1.d1', '90.a1.a1'], 'normal_contains': ['540.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '180.36', 'quotient_action_image': '1.1', 'quotient_action_kernel': '180.36', 'quotient_action_kernel_order': 180, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108124259
    {'ambient': '540.76', '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', '90.d1.a1', '90.d1.e1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3495, -1, 4409, -1, 6200, -1, 2385, -1], 'generators': [366], 'label': '540.76.180.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': '540.76', '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: 108124260
    {'ambient': '540.76', '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', '90.d1.b1', '90.d1.f1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3495, -1, 1199, -1, 6200, -1, 6521, -1], 'generators': [194], 'label': '540.76.180.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': '540.76', '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: 108124261
    {'ambient': '540.76', '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', '90.d1.c1', '90.d1.g1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3495, -1, 5792, -1, 6200, -1, 3095, -1], 'generators': [368], 'label': '540.76.180.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': '540.76', '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: 108124262
    {'ambient': '540.76', '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', '90.d1.d1', '90.d1.h1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3495, -1, 8112, -1, 6200, -1, 8683, -1], 'generators': [2], 'label': '540.76.180.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': '540.76', '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: 108124263
    {'ambient': '540.76', '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': ['2.b1.b1', '2.b1.a1'], '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': [6143, 2490, 6087, 7392, 6752, 8450, 3978, 6324], 'generators': [270], 'label': '540.76.270.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: 108124264
    {'ambient': '540.76', 'aut_centralizer_order': 192, 'aut_label': '270.b1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 17280, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '90.c1.a1', '90.d1.a1', '90.d1.b1', '90.d1.c1', '90.d1.d1', '135.a1.a1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7563, -1, 7720, -1, 7857, -1, 4146, -1], 'generators': [271], 'label': '540.76.270.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '270.b1.a1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108124265
    {'ambient': '540.76', 'aut_centralizer_order': 192, 'aut_label': '270.b1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '1.1', 'aut_weyl_index': 17280, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.b1', '90.c1.b1', '90.d1.e1', '90.d1.f1', '90.d1.g1', '90.d1.h1', '135.a1.a1'], 'contains': ['540.a1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7563, -1, 4309, -1, 7857, -1, 3810, -1], 'generators': [1], 'label': '540.76.270.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '270.b1.b1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '270.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108124266
    {'ambient': '540.76', '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': ['90.d1.h1', '90.d1.g1', '90.d1.f1', '90.d1.d1', '90.d1.c1', '90.d1.b1'], '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': [3642, 3307, 5078, 6736, 4383, 8670, 2077, 7049], 'generators': [270, 6, 108, 366], 'label': '540.76.6.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'}
  • id: 108124267
    {'ambient': '540.76', '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', '270.b1.a1', '270.b1.b1'], 'contains': [], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6143, 2490, 4715, 7392, 6752, 7128, 3978, 5077], 'generators': [], 'label': '540.76.540.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': '540.76', '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: 108124268
    {'ambient': '540.76', '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': ['90.d1.e1', '90.d1.h1', '90.d1.g1', '90.d1.a1', '90.d1.d1', '90.d1.c1'], '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': [3642, 3307, 1539, 2572, 4383, 8670, 5781, 4613], 'generators': [270, 6, 108, 194], 'label': '540.76.6.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: 108124269
    {'ambient': '540.76', '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': ['90.d1.e1', '90.d1.f1', '90.d1.h1', '90.d1.a1', '90.d1.b1', '90.d1.d1'], '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': [3642, 3307, 5937, 8731, 4383, 8670, 3543, 3396], 'generators': [270, 6, 108, 368], 'label': '540.76.6.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: 108124270
    {'ambient': '540.76', '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': ['90.d1.e1', '90.d1.g1', '90.d1.f1', '90.d1.a1', '90.d1.c1', '90.d1.b1'], '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': [3642, 3307, 6612, 3998, 4383, 8670, 8431, 5831], 'generators': [270, 6, 108, 2], 'label': '540.76.6.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: 108124271
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.c1.a1', '18.d1.a1', '30.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 8159, -1, 6676, -1, 2460, -1], 'generators': [271, 366, 108, 6], 'label': '540.76.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124272
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.b1'], 'contains': ['12.a1.b1', '18.c1.a1', '18.d1.b1', '30.b1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 3744, -1, 6676, -1, 6371, -1], 'generators': [271, 188, 108, 6], 'label': '540.76.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.b1.b1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124273
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.c1'], 'contains': ['12.a1.c1', '18.c1.a1', '18.d1.c1', '30.b1.c1'], 'core': '12.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 9038, -1, 6676, -1, 3926, -1], 'generators': [271, 374, 108, 6], 'label': '540.76.6.b1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '6.b1.c1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124274
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.d1'], 'contains': ['12.a1.d1', '18.c1.a1', '18.d1.d1', '30.b1.d1'], 'core': '12.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 9550, -1, 6676, -1, 8814, -1], 'generators': [271, 2, 108, 6], 'label': '540.76.6.b1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '6.b1.d1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.d1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124275
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '18.c1.b1', '18.d1.e1', '30.b1.e1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 2809, -1, 6676, -1, 1694, -1], 'generators': [1, 366, 108, 6], 'label': '540.76.6.b1.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.e1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.e1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124276
    {'ambient': '540.76', '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': ['270.b1.b1', '270.b1.a1'], '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': [1202, 4980, 5051, 3998, 1867, 5587, 5297, 4890], 'generators': [270, 366, 108, 2, 6], 'label': '540.76.2.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.a1', '6.a1.b1', '6.a1.d1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '90.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108124277
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.b1'], 'contains': ['12.a1.b1', '18.c1.b1', '18.d1.f1', '30.b1.f1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 1073, -1, 6676, -1, 5398, -1], 'generators': [1, 188, 108, 6], 'label': '540.76.6.b1.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.b1.f1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.f1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124278
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.c1'], 'contains': ['12.a1.c1', '18.c1.b1', '18.d1.g1', '30.b1.g1'], 'core': '12.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 3376, -1, 6676, -1, 3161, -1], 'generators': [1, 374, 108, 6], 'label': '540.76.6.b1.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '6.b1.g1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.g1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124279
    {'ambient': '540.76', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '240.195', 'aut_weyl_index': 72, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.d1'], 'contains': ['12.a1.d1', '18.c1.b1', '18.d1.h1', '30.b1.h1'], 'core': '12.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [4856, -1, 4367, -1, 6676, -1, 8048, -1], 'generators': [1, 2, 108, 6], 'label': '540.76.6.b1.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '6.b1.h1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.h1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124280
    {'ambient': '540.76', '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', '18.c1.a1', '18.c1.b1', '27.a1.a1', '45.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8658, -1, 7678, -1, 7834, -1, 4279, -1], 'generators': [1, 6, 108, 270], 'label': '540.76.9.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: 108124281
    {'ambient': '540.76', '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', '18.d1.a1', '18.d1.e1', '27.a1.a1', '45.b1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5603, -1, 6386, -1, 8700, -1, 592, -1], 'generators': [1, 366, 108, 270], 'label': '540.76.9.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: 108124282
    {'ambient': '540.76', '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', '18.d1.b1', '18.d1.f1', '27.a1.a1', '45.b1.b1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5603, -1, 757, -1, 8700, -1, 6075, -1], 'generators': [1, 188, 108, 270], 'label': '540.76.9.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: 108124283
    {'ambient': '540.76', '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', '18.d1.c1', '18.d1.g1', '27.a1.a1', '45.b1.c1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5603, -1, 7336, -1, 8700, -1, 1344, -1], 'generators': [1, 374, 108, 270], 'label': '540.76.9.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: 108124284
    {'ambient': '540.76', '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', '18.d1.d1', '18.d1.h1', '27.a1.a1', '45.b1.d1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5603, -1, 8769, -1, 8700, -1, 9482, -1], 'generators': [1, 2, 108, 270], 'label': '540.76.9.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: 108124285
    {'ambient': '540.76', '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': ['54.b1.b1', '54.b1.a1'], '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': [647, 8386, 4486, 1557, 671, 5404, 7051, 8379], 'generators': [270, 2, 366, 6], 'label': '540.76.10.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.a1', '30.a1.b1', '30.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '90.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108124286
    {'ambient': '540.76', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '432.734', 'aut_weyl_index': 40, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.b1.a1', '30.b1.b1', '30.b1.c1', '30.b1.d1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1779, -1, 7007, -1, 3324, -1, 7408, -1], 'generators': [271, 2, 366, 6], 'label': '540.76.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108124287
    {'ambient': '540.76', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8640.be', 'aut_weyl_index': 2, 'centralizer': '90.a1.a1', 'complements': ['270.a1.a1', '270.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '6.b1.d1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2770, 9203, 6980, 5853, 4927, 1697, 5792, 1789], 'generators': [271, 366, 108, 2, 6], 'label': '540.76.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '180.36', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '90.9'}
  • id: 108124288
    {'ambient': '540.76', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '432.734', 'aut_weyl_index': 40, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.b1.e1', '30.b1.f1', '30.b1.g1', '30.b1.h1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1779, -1, 2156, -1, 3324, -1, 6693, -1], 'generators': [1, 2, 366, 6], 'label': '540.76.10.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 108124289
    {'ambient': '540.76', '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.d1', '45.b1.c1', '45.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.b1.e1'], 'contains': ['36.a1.a1', '36.b1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3642, 6075, 3376, 7620, 3033, 4028, 1965, 4195], 'generators': [366, 108, 6], 'label': '540.76.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, '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': '180.36', '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: 108124290
    {'ambient': '540.76', '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.d1', '45.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.b1', '6.b1.b1', '6.b1.f1'], 'contains': ['36.a1.a1', '36.b1.b1', '60.a1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3642, 6075, 1283, 3429, 3033, 4028, 6002, 1759], 'generators': [194, 108, 6], 'label': '540.76.12.a1.b1', 'mobius_quo': 0, 'mobius_sub': -6, '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': '180.36', '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: 108124291
    {'ambient': '540.76', '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.b1', '45.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.c1', '6.b1.c1', '6.b1.g1'], 'contains': ['36.a1.a1', '36.b1.c1', '60.a1.c1'], 'core': '12.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3642, 6075, 3914, 9721, 3033, 4028, 3296, 542], 'generators': [368, 108, 6], 'label': '540.76.12.a1.c1', 'mobius_quo': 0, 'mobius_sub': -6, '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': '180.36', '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: 108124292
    {'ambient': '540.76', '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.c1', '45.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.d1', '6.b1.d1', '6.b1.h1'], 'contains': ['36.a1.a1', '36.b1.d1', '60.a1.d1'], 'core': '12.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3642, 6075, 5057, 4855, 3033, 4028, 8088, 2977], 'generators': [2, 108, 6], 'label': '540.76.12.a1.d1', 'mobius_quo': 0, 'mobius_sub': -6, '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': '180.36', '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: 108124293
    {'ambient': '540.76', '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', '30.b1.a1', '30.b1.e1', '45.a1.a1', '45.b1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3066, -1, 5339, -1, 5525, -1, 2810, -1], 'generators': [1, 270, 6, 366], 'label': '540.76.15.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: 108124294
    {'ambient': '540.76', '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', '30.b1.b1', '30.b1.f1', '45.a1.a1', '45.b1.b1'], 'core': '30.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [3066, -1, 1613, -1, 5525, -1, 7698, -1], 'generators': [1, 270, 6, 188], 'label': '540.76.15.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: 108124295
    {'ambient': '540.76', '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', '30.b1.c1', '30.b1.g1', '45.a1.a1', '45.b1.c1'], 'core': '30.a1.c1', 'coset_action_label': None, 'count': 15, 'diagramx': [3066, -1, 7118, -1, 5525, -1, 4597, -1], 'generators': [1, 270, 6, 374], 'label': '540.76.15.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: 108124296
    {'ambient': '540.76', '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', '30.b1.d1', '30.b1.h1', '45.a1.a1', '45.b1.d1'], 'core': '30.a1.d1', 'coset_action_label': None, 'count': 15, 'diagramx': [3066, -1, 7935, -1, 5525, -1, 9164, -1], 'generators': [1, 270, 6, 2], 'label': '540.76.15.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: 108124297
    {'ambient': '540.76', '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': [6639, 2669, 5677, 7287, 5035, 8835, 3910, 5675], 'generators': [270, 108, 6], 'label': '540.76.18.a1.a1', 'mobius_quo': -1, 'mobius_sub': -27, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.c1', '6.a1.a1', '6.a1.b1', '6.a1.d1'], '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: 108124298
    {'ambient': '540.76', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8640.be', 'aut_weyl_index': 2, 'centralizer': '90.a1.a1', 'complements': ['270.a1.a1', '270.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.e1', '6.b1.f1', '6.b1.g1', '6.b1.h1', '10.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2770, 9203, 2827, 7628, 4927, 1697, 4802, 3306], 'generators': [1, 366, 108, 2, 6], 'label': '540.76.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '180.36', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '90.9'}
  • id: 108124299
    {'ambient': '540.76', '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': [4856, -1, 5480, -1, 7811, -1, 291, -1], 'generators': [270, 108, 366], 'label': '540.76.18.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: 108124300
    {'ambient': '540.76', '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': [4856, -1, 705, -1, 7811, -1, 6297, -1], 'generators': [270, 108, 194], 'label': '540.76.18.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: 108124301
    {'ambient': '540.76', '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': [4856, -1, 6758, -1, 7811, -1, 1085, -1], 'generators': [270, 108, 368], 'label': '540.76.18.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: 108124302
    {'ambient': '540.76', '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': [4856, -1, 8783, -1, 7811, -1, 9540, -1], 'generators': [270, 108, 2], 'label': '540.76.18.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: 108124303
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 432, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.b1.b1', '6.b1.c1', '6.b1.d1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.b1.a1', '90.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8421, -1, 9579, -1, 6944, -1, 4809, -1], 'generators': [271, 108, 6], 'label': '540.76.18.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 108124304
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '40.12', 'aut_weyl_index': 432, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.e1', '6.b1.f1', '6.b1.g1', '6.b1.h1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.b1.b1', '90.c1.b1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8421, -1, 2863, -1, 6944, -1, 3646, -1], 'generators': [1, 108, 6], 'label': '540.76.18.c1.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.b1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 108124305
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.b1.a1'], 'contains': ['36.b1.a1', '54.b1.a1', '90.d1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 7810, -1, 9045, -1, 499, -1], 'generators': [271, 108, 366], 'label': '540.76.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124306
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '9.b1.b1'], 'contains': ['36.b1.b1', '54.b1.a1', '90.d1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 1813, -1, 9045, -1, 6504, -1], 'generators': [271, 108, 188], 'label': '540.76.18.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.d1.b1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124307
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '9.b1.c1'], 'contains': ['36.b1.c1', '54.b1.a1', '90.d1.c1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 9153, -1, 9045, -1, 1292, -1], 'generators': [271, 108, 374], 'label': '540.76.18.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '18.d1.c1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.c1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124308
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.d1', '9.b1.d1'], 'contains': ['36.b1.d1', '54.b1.a1', '90.d1.d1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 9920, -1, 9045, -1, 9748, -1], 'generators': [271, 108, 2], 'label': '540.76.18.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '18.d1.d1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.d1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124309
    {'ambient': '540.76', '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', '6.b1.a1', '6.b1.e1', '9.a1.a1', '9.b1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4346, -1, 5979, -1, 6561, -1, 2460, -1], 'generators': [1, 6, 366, 270, 108], 'label': '540.76.3.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: 108124310
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.e1', '9.b1.a1'], 'contains': ['36.b1.a1', '54.b1.b1', '90.d1.e1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 3800, -1, 9045, -1, 83, -1], 'generators': [1, 108, 366], 'label': '540.76.18.d1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.d1.e1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.e1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124311
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.f1', '9.b1.b1'], 'contains': ['36.b1.b1', '54.b1.b1', '90.d1.f1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 80, -1, 9045, -1, 5708, -1], 'generators': [1, 108, 188], 'label': '540.76.18.d1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.d1.f1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.f1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124312
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.g1', '9.b1.c1'], 'contains': ['36.b1.c1', '54.b1.b1', '90.d1.g1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 5110, -1, 9045, -1, 877, -1], 'generators': [1, 108, 374], 'label': '540.76.18.d1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.c1', 'old_label': '18.d1.g1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.g1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124313
    {'ambient': '540.76', 'aut_centralizer_order': 6, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '120.36', 'aut_weyl_index': 144, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.h1', '9.b1.d1'], 'contains': ['36.b1.d1', '54.b1.b1', '90.d1.h1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5795, -1, 6558, -1, 9045, -1, 9332, -1], 'generators': [1, 108, 2], 'label': '540.76.18.d1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.d1', 'old_label': '18.d1.h1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.h1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
  • id: 108124314
    {'ambient': '540.76', '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', '10.b1.a1', '10.b1.b1'], 'contains': ['60.a1.a1', '60.a1.b1', '60.a1.c1', '60.a1.d1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [795, 9462, 2678, 394, 1085, 1862, 6693, 5077], 'generators': [2, 366], 'label': '540.76.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['60.a1.c1', '60.a1.a1', '60.a1.b1', '60.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '180.36', '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: 108124315
    {'ambient': '540.76', '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', '54.b1.a1', '54.b1.b1', '135.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9353, -1, 8352, -1, 9728, -1, 1671, -1], 'generators': [1, 108, 270], 'label': '540.76.27.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: 108124316
    {'ambient': '540.76', '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': ['18.d1.h1', '18.d1.g1', '18.d1.f1', '18.d1.d1', '18.d1.c1', '18.d1.b1'], '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': [1897, 5876, 4385, 4252, 1883, 6780, 2631, 9559], 'generators': [270, 366, 6], 'label': '540.76.30.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: 108124317
    {'ambient': '540.76', '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': ['18.d1.e1', '18.d1.h1', '18.d1.g1', '18.d1.a1', '18.d1.d1', '18.d1.c1'], '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': [1897, 5876, 1376, 1540, 1883, 6780, 7254, 7527], 'generators': [270, 194, 6], 'label': '540.76.30.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: 108124318
    {'ambient': '540.76', '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': ['18.d1.e1', '18.d1.f1', '18.d1.h1', '18.d1.a1', '18.d1.b1', '18.d1.d1'], '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': [1897, 5876, 6188, 6107, 1883, 6780, 4489, 6511], 'generators': [270, 368, 6], 'label': '540.76.30.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: 108124319
    {'ambient': '540.76', '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': ['18.d1.e1', '18.d1.g1', '18.d1.f1', '18.d1.a1', '18.d1.c1', '18.d1.b1'], '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': [1897, 5876, 7005, 2730, 1883, 6780, 8753, 8543], 'generators': [270, 2, 6], 'label': '540.76.30.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: 108124320
    {'ambient': '540.76', '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', '6.b1.b1', '6.b1.f1', '9.a1.a1', '9.b1.b1', '15.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4346, -1, 1766, -1, 6561, -1, 6222, -1], 'generators': [1, 6, 188, 270, 108], 'label': '540.76.3.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: 108124321
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '90.c1.a1', '90.d1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 7394, -1, 4176, -1, 2948, -1], 'generators': [271, 6, 366], 'label': '540.76.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124322
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.b1.a1', '15.a1.b1'], 'contains': ['60.a1.b1', '90.c1.a1', '90.d1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 4691, -1, 4176, -1, 7740, -1], 'generators': [271, 6, 188], 'label': '540.76.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '30.b1.b1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124323
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.c1', '10.b1.a1', '15.a1.c1'], 'contains': ['60.a1.c1', '90.c1.a1', '90.d1.c1'], 'core': '60.a1.c1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 8296, -1, 4176, -1, 5127, -1], 'generators': [271, 6, 374], 'label': '540.76.30.b1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.c1', 'old_label': '30.b1.c1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124324
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.d1', '10.b1.a1', '15.a1.d1'], 'contains': ['60.a1.d1', '90.c1.a1', '90.d1.d1'], 'core': '60.a1.d1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 8942, -1, 4176, -1, 9071, -1], 'generators': [271, 6, 2], 'label': '540.76.30.b1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.d1', 'old_label': '30.b1.d1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124325
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.e1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.a1.a1', '90.c1.b1', '90.d1.e1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 1937, -1, 4176, -1, 2313, -1], 'generators': [1, 6, 366], 'label': '540.76.30.b1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.e1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124326
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.f1', '10.b1.b1', '15.a1.b1'], 'contains': ['60.a1.b1', '90.c1.b1', '90.d1.f1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 985, -1, 4176, -1, 6936, -1], 'generators': [1, 6, 188], 'label': '540.76.30.b1.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '30.b1.f1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124327
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.g1', '10.b1.b1', '15.a1.c1'], 'contains': ['60.a1.c1', '90.c1.b1', '90.d1.g1'], 'core': '60.a1.c1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 2326, -1, 4176, -1, 4172, -1], 'generators': [1, 6, 374], 'label': '540.76.30.b1.g1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.c1', 'old_label': '30.b1.g1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124328
    {'ambient': '540.76', 'aut_centralizer_order': 12, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1440, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.h1', '10.b1.b1', '15.a1.d1'], 'contains': ['60.a1.d1', '90.c1.b1', '90.d1.h1'], 'core': '60.a1.d1', 'coset_action_label': None, 'count': 15, 'diagramx': [2903, -1, 3910, -1, 4176, -1, 8436, -1], 'generators': [1, 6, 2], 'label': '540.76.30.b1.h1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.d1', 'old_label': '30.b1.h1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124329
    {'ambient': '540.76', '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', '18.c1.a1', '18.c1.b1'], 'contains': ['108.a1.a1', '180.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6172, 2550, 3233, 8198, 5035, 5807, 4291, 3216], 'generators': [6, 108], 'label': '540.76.36.a1.a1', 'mobius_quo': 1, 'mobius_sub': 54, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.c1', '12.a1.a1', '12.a1.b1', '12.a1.d1', '18.a1.a1'], 'normal_contains': ['108.a1.a1', '180.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '180.36', '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: 108124330
    {'ambient': '540.76', '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', '18.d1.a1', '18.d1.e1'], 'contains': ['108.a1.a1', '180.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4678, -1, 4802, -1, 6814, -1, 1222, -1], 'generators': [366, 108], 'label': '540.76.36.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': '540.76', '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: 108124331
    {'ambient': '540.76', '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', '6.b1.c1', '6.b1.g1', '9.a1.a1', '9.b1.c1', '15.a1.c1'], 'core': '6.a1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4346, -1, 7207, -1, 6561, -1, 3926, -1], 'generators': [1, 6, 374, 270, 108], 'label': '540.76.3.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: 108124332
    {'ambient': '540.76', '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', '18.d1.b1', '18.d1.f1'], 'contains': ['108.a1.a1', '180.b1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4678, -1, 378, -1, 6814, -1, 6084, -1], 'generators': [194, 108], 'label': '540.76.36.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': '540.76', '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: 108124333
    {'ambient': '540.76', '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', '18.d1.c1', '18.d1.g1'], 'contains': ['108.a1.a1', '180.b1.c1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4678, -1, 5510, -1, 6814, -1, 2656, -1], 'generators': [368, 108], 'label': '540.76.36.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': '540.76', '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: 108124334
    {'ambient': '540.76', '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', '18.d1.d1', '18.d1.h1'], 'contains': ['108.a1.a1', '180.b1.d1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4678, -1, 8698, -1, 6814, -1, 8590, -1], 'generators': [2, 108], 'label': '540.76.36.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': '540.76', '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: 108124335
    {'ambient': '540.76', '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', '90.c1.a1', '90.c1.b1', '135.a1.a1'], 'core': '90.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7600, -1, 7225, -1, 5894, -1, 5444, -1], 'generators': [1, 270, 6], 'label': '540.76.45.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: 108124336
    {'ambient': '540.76', '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', '90.d1.a1', '90.d1.e1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4234, -1, 5834, -1, 8424, -1, 688, -1], 'generators': [1, 270, 366], 'label': '540.76.45.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: 108124337
    {'ambient': '540.76', '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', '90.d1.b1', '90.d1.f1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4234, -1, 846, -1, 8424, -1, 7497, -1], 'generators': [1, 270, 188], 'label': '540.76.45.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: 108124338
    {'ambient': '540.76', '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', '90.d1.c1', '90.d1.g1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4234, -1, 7969, -1, 8424, -1, 1482, -1], 'generators': [1, 270, 374], 'label': '540.76.45.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: 108124339
    {'ambient': '540.76', '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', '90.d1.d1', '90.d1.h1', '135.a1.a1'], 'core': '270.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4234, -1, 8935, -1, 8424, -1, 9937, -1], 'generators': [1, 270, 2], 'label': '540.76.45.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: 108124340
    {'ambient': '540.76', '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': ['10.b1.b1', '10.b1.a1'], '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': [7053, 1035, 6695, 8417, 8040, 8743, 3534, 6324], 'generators': [270, 108], 'label': '540.76.54.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: 108124341
    {'ambient': '540.76', 'aut_centralizer_order': 48, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 864, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.d1.a1', '18.d1.b1', '18.d1.c1', '18.d1.d1', '27.a1.a1'], 'contains': ['108.a1.a1', '270.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9086, -1, 9691, -1, 9283, -1, 3721, -1], 'generators': [271, 108], 'label': '540.76.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 108124342
    {'ambient': '540.76', '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', '6.b1.d1', '6.b1.h1', '9.a1.a1', '9.b1.d1', '15.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': [4346, -1, 7678, -1, 6561, -1, 8431, -1], 'generators': [1, 6, 2, 270, 108], 'label': '540.76.3.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: 108124343
    {'ambient': '540.76', 'aut_centralizer_order': 48, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '20.3', 'aut_weyl_index': 864, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '18.d1.e1', '18.d1.f1', '18.d1.g1', '18.d1.h1', '27.a1.a1'], 'contains': ['108.a1.a1', '270.b1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9086, -1, 4220, -1, 9283, -1, 3347, -1], 'generators': [1, 108], 'label': '540.76.54.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.b1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.b1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
  • id: 108124344
    {'ambient': '540.76', '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.d1', '9.b1.c1', '9.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1', '30.b1.a1', '30.b1.e1'], 'contains': ['180.a1.a1', '180.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1897, 7211, 2551, 4514, 3432, 4174, 4092, 5689], 'generators': [366, 6], 'label': '540.76.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 30, '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': '180.36', '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: 108124345
    {'ambient': '540.76', '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.d1', '9.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '20.a1.a1', '30.a1.b1', '30.b1.b1', '30.b1.f1'], 'contains': ['180.a1.a1', '180.b1.b1'], 'core': '60.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1897, 7211, 1436, 279, 3432, 4174, 6612, 4464], 'generators': [194, 6], 'label': '540.76.60.a1.b1', 'mobius_quo': 0, 'mobius_sub': 30, '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': '180.36', '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: 108124346
    {'ambient': '540.76', '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.b1', '9.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.c1', '20.a1.a1', '30.a1.c1', '30.b1.c1', '30.b1.g1'], 'contains': ['180.a1.a1', '180.b1.c1'], 'core': '60.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1897, 7211, 3495, 5573, 3432, 4174, 4489, 3851], 'generators': [368, 6], 'label': '540.76.60.a1.c1', 'mobius_quo': 0, 'mobius_sub': 30, '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': '180.36', '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: 108124347
    {'ambient': '540.76', '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.c1', '9.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.d1', '20.a1.a1', '30.a1.d1', '30.b1.d1', '30.b1.h1'], 'contains': ['180.a1.a1', '180.b1.d1'], 'core': '60.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1897, 7211, 5065, 2992, 3432, 4174, 8391, 5077], 'generators': [2, 6], 'label': '540.76.60.a1.d1', 'mobius_quo': 0, 'mobius_sub': 30, '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': '180.36', '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: 108124348
    {'ambient': '540.76', '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': [5588, 4362, 6040, 5880, 4421, 7275, 4837, 6922], 'generators': [270, 6], 'label': '540.76.90.a1.a1', 'mobius_quo': 1, 'mobius_sub': 135, 'normal_closure': '90.a1.a1', 'normal_contained_in': ['18.a1.a1', '30.a1.c1', '30.a1.a1', '30.a1.b1', '30.a1.d1'], '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: 108124349
    {'ambient': '540.76', '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': [3620, -1, 5462, -1, 6200, -1, 2301, -1], 'generators': [270, 366], 'label': '540.76.90.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: 108124350
    {'ambient': '540.76', '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': [3620, -1, 1060, -1, 6200, -1, 6792, -1], 'generators': [270, 194], 'label': '540.76.90.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: 108124351
    {'ambient': '540.76', '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': [3620, -1, 6921, -1, 6200, -1, 3011, -1], 'generators': [270, 368], 'label': '540.76.90.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: 108124352
    {'ambient': '540.76', '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': [3620, -1, 8797, -1, 6200, -1, 8945, -1], 'generators': [270, 2], 'label': '540.76.90.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: 108124353
    {'ambient': '540.76', 'aut_centralizer_order': 10, 'aut_label': '4.a1', 'aut_quo_index': 3, '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', '2.b1.a1', '2.b1.b1'], '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': [1335, 8247, 3172, 5853, 2151, 1862, 4980, 2066], 'generators': [2, 108, 6, 366], 'label': '540.76.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['12.a1.c1', '12.a1.a1', '12.a1.b1', '12.a1.d1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '180.36', '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: 108124354
    {'ambient': '540.76', 'aut_centralizer_order': 96, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.b1.a1', '30.b1.b1', '30.b1.c1', '30.b1.d1', '45.a1.a1'], 'contains': ['180.a1.a1', '270.b1.a1'], 'core': '180.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7926, -1, 7901, -1, 5648, -1, 5066, -1], 'generators': [271, 6], 'label': '540.76.90.c1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.c1.a1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108124355
    {'ambient': '540.76', 'aut_centralizer_order': 96, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': 90, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8640, 'centralizer': '45.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '30.b1.e1', '30.b1.f1', '30.b1.g1', '30.b1.h1', '45.a1.a1'], 'contains': ['180.a1.a1', '270.b1.b1'], 'core': '180.a1.a1', 'coset_action_label': None, 'count': 45, 'diagramx': [7926, -1, 1954, -1, 5648, -1, 4669, -1], 'generators': [1, 6], 'label': '540.76.90.c1.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1.a1', 'old_label': '90.c1.b1', 'projective_image': '180.36', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 108124356
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '30.b1.a1', '45.b1.a1'], 'contains': ['180.b1.a1', '270.b1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 6666, -1, 7427, -1, 2469, -1], 'generators': [271, 366], 'label': '540.76.90.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.d1.a1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124357
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '30.b1.b1', '45.b1.b1'], 'contains': ['180.b1.b1', '270.b1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 1571, -1, 7427, -1, 6960, -1], 'generators': [271, 188], 'label': '540.76.90.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '90.d1.b1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124358
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.c1', '30.b1.c1', '45.b1.c1'], 'contains': ['180.b1.c1', '270.b1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 8626, -1, 7427, -1, 3179, -1], 'generators': [271, 374], 'label': '540.76.90.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.c1', 'old_label': '90.d1.c1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124359
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.d1', '30.b1.d1', '45.b1.d1'], 'contains': ['180.b1.d1', '270.b1.a1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 9175, -1, 7427, -1, 9113, -1], 'generators': [271, 2], 'label': '540.76.90.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.d1', 'old_label': '90.d1.d1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124360
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.e1', '30.b1.e1', '45.b1.a1'], 'contains': ['180.b1.a1', '270.b1.b1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 3630, -1, 7427, -1, 2133, -1], 'generators': [1, 366], 'label': '540.76.90.d1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.d1.e1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124361
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.f1', '30.b1.f1', '45.b1.b1'], 'contains': ['180.b1.b1', '270.b1.b1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 339, -1, 7427, -1, 6432, -1], 'generators': [1, 188], 'label': '540.76.90.d1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.b1', 'old_label': '90.d1.f1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124362
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.g1', '30.b1.g1', '45.b1.c1'], 'contains': ['180.b1.c1', '270.b1.b1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 5709, -1, 7427, -1, 2843, -1], 'generators': [1, 374], 'label': '540.76.90.d1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.c1', 'old_label': '90.d1.g1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 108124363
    {'ambient': '540.76', 'aut_centralizer_order': 24, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '6.1', 'aut_weyl_index': 2880, 'centralizer': '90.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.h1', '30.b1.h1', '45.b1.d1'], 'contains': ['180.b1.d1', '270.b1.b1'], 'core': '540.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4338, -1, 6287, -1, 7427, -1, 8776, -1], 'generators': [1, 2], 'label': '540.76.90.d1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.d1', 'old_label': '90.d1.h1', 'projective_image': '540.76', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}