Abstract group data - 1889568.ij

Formats: - HTML - YAML - JSON - 2026-02-03T18:04:51.822551

• 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': '6.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[806638059760198036614658940, 435557187109449513781389661], [806648185024956916970749728, 435557187827184911028756061], [1396708047118523133773334224, 521257695501129290729671261], [806638059280146921559695740, 435563975630170642989933661], [806648185748406932157519740, 435564026721132431172064861], [1257085798281772625906703740, 2249216564265169805447412061], [6455145235900049495123881340, 5785762384241114936837344861], [806638059760198036614866898, 435557187109449513781416400], [806638059760198036614884784, 435557187109449513781532842], [806638059760198036614826102, 435557187109449513781394130], [3629705314754865935111938940, 638058183221040302628276061], [3382170308280190773272598140, 5887189971145822026885165661], [3637174652609402375208553340, 439286470774217434407156061], [3234506712475336728236847740, 439281096372099040170228061], [3637211447339112400537743740, 503551262892246259894202461], [806664261628244215324892540, 435563777962927858122996061], [806648178328096426554447740, 435564026118932692140276061], [806638059760198036614808905, 435557187109449513781389661], [806638059760198036614851024, 435557187109449513781389661], [806638059760198036614648944, 435557187109449513781389661], [419063464310912853528267421, 1257107769820206873015229896]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 136048896, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 216.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 54, 1, 1], [2, 243, 1, 1], [2, 486, 1, 1], [2, 2916, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 6, 3, 1], [3, 8, 2, 1], [3, 8, 4, 1], [3, 12, 1, 2], [3, 12, 2, 1], [3, 12, 6, 1], [3, 12, 18, 1], [3, 16, 2, 1], [3, 24, 1, 3], [3, 24, 2, 2], [3, 24, 3, 1], [3, 24, 4, 1], [3, 24, 6, 2], [3, 24, 9, 1], [3, 24, 12, 1], [3, 24, 18, 2], [3, 32, 1, 1], [3, 32, 2, 2], [3, 48, 1, 2], [3, 48, 2, 3], [3, 48, 4, 2], [3, 48, 6, 1], [3, 48, 12, 2], [3, 48, 18, 1], [3, 48, 36, 2], [3, 96, 1, 2], [3, 96, 2, 4], [3, 96, 3, 1], [3, 96, 4, 1], [3, 96, 6, 3], [3, 96, 9, 1], [3, 96, 12, 1], [3, 96, 18, 1], [3, 96, 36, 1], [3, 11664, 2, 1], [4, 78732, 1, 1], [6, 54, 2, 1], [6, 54, 6, 1], [6, 54, 18, 1], [6, 108, 1, 2], [6, 108, 2, 3], [6, 108, 4, 1], [6, 108, 6, 2], [6, 108, 12, 1], [6, 108, 18, 2], [6, 108, 36, 1], [6, 216, 1, 2], [6, 216, 2, 5], [6, 216, 4, 3], [6, 216, 6, 2], [6, 216, 12, 3], [6, 216, 18, 2], [6, 216, 36, 3], [6, 432, 1, 1], [6, 432, 2, 3], [6, 432, 4, 2], [6, 432, 6, 1], [6, 432, 12, 2], [6, 432, 18, 1], [6, 432, 36, 2], [6, 486, 1, 1], [6, 486, 2, 1], [6, 486, 3, 1], [6, 486, 6, 1], [6, 486, 9, 1], [6, 486, 18, 1], [6, 972, 1, 2], [6, 972, 2, 2], [6, 972, 4, 1], [6, 972, 6, 1], [6, 972, 12, 1], [6, 972, 18, 1], [6, 972, 36, 1], [6, 1944, 1, 2], [6, 1944, 2, 1], [6, 1944, 3, 1], [6, 1944, 6, 1], [6, 1944, 9, 1], [6, 1944, 18, 1], [6, 11664, 2, 1], [6, 17496, 1, 1], [6, 34992, 1, 1], [6, 104976, 2, 1], [9, 11664, 4, 1], [9, 23328, 2, 2], [9, 23328, 4, 3], [9, 23328, 8, 1], [12, 157464, 1, 1], [18, 104976, 4, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 54, 1], [2, 243, 1], [2, 486, 1], [2, 2916, 1], [3, 2, 1], [3, 6, 4], [3, 8, 6], [3, 12, 28], [3, 16, 2], [3, 24, 83], [3, 32, 5], [3, 48, 136], [3, 96, 110], [3, 11664, 2], [4, 78732, 1], [6, 54, 26], [6, 108, 108], [6, 216, 216], [6, 432, 135], [6, 486, 39], [6, 972, 82], [6, 1944, 40], [6, 11664, 2], [6, 17496, 1], [6, 34992, 1], [6, 104976, 2], [9, 11664, 4], [9, 23328, 24], [12, 157464, 1], [18, 104976, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1889568.ij', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 15, 'conjugacy_classes_known': False, 'counter': 218, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 54, 1, 1], [2, 243, 1, 1], [2, 486, 1, 1], [2, 2916, 1, 1], [3, 2, 1, 1], [3, 6, 1, 4], [3, 8, 2, 3], [3, 12, 1, 2], [3, 12, 2, 13], [3, 16, 2, 1], [3, 24, 1, 15], [3, 24, 2, 34], [3, 32, 1, 3], [3, 32, 2, 1], [3, 48, 1, 4], [3, 48, 2, 66], [3, 96, 1, 22], [3, 96, 2, 44], [3, 11664, 2, 1], [4, 78732, 1, 1], [6, 54, 2, 13], [6, 108, 1, 4], [6, 108, 2, 52], [6, 216, 1, 6], [6, 216, 2, 105], [6, 432, 1, 3], [6, 432, 2, 66], [6, 486, 1, 13], [6, 486, 2, 13], [6, 972, 1, 4], [6, 972, 2, 39], [6, 1944, 1, 14], [6, 1944, 2, 13], [6, 11664, 2, 1], [6, 17496, 1, 1], [6, 34992, 1, 1], [6, 104976, 2, 1], [9, 11664, 2, 2], [9, 23328, 2, 12], [12, 157464, 1, 1], [18, 104976, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [10, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 144], [24, 0, 210], [24, 1, 18], [48, 0, 180], [96, 0, 60], [96, 1, 15]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '209952.y', 'hash': 2174946664390704901, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [18, 6], 'inner_gens': [[806638059760198036614658940, 2109794389966348227518980024], [3290887051609446803047003789, 435557187109449513781389661]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 1889568, 'inner_split': None, 'inner_tex': 'C_3^9.C_2^4.C_6', 'inner_used': None, 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 6], [2, 3], [3, 2], [6, 71], [8, 18], [12, 220], [16, 12], [24, 339], [32, 15], [48, 272], [96, 110]], 'label': '1889568.ij', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^9.C2^4.C6', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 144, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 1068, 'number_divisions': 586, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1889568, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3699], [3, 43010], [4, 78732], [6, 580230], [9, 606528], [12, 157464], [18, 419904]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '72.48', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 72, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_6\\times D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 3], [3, 2], [4, 1], [6, 19], [12, 38], [16, 9], [24, 139], [32, 9], [48, 160], [64, 6], [96, 154], [192, 44]], 'representations': {'PC': {'code': '1155175612621707185415403814667519054149451115622517054424581820595084361892500774210817078461329002525348963689803096324662271178417963768647925166511392360816250552604997633092576341443398119966229971995966938052364855342149450586511736266800808862175124424607954771175195265671370397681253549151094277280683515875600134943324964253596202494059188207702097674557208592936544540244881262053168683000773151895631183673868324943973359637246945983', 'gens': [1, 3, 5, 7, 9, 11, 12, 13, 14, 15], 'pres': [15, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 30, 807032, 10736972, 122, 71073363, 43081218, 89678254, 52969519, 15649684, 5346274, 214, 12138125, 40986560, 16563995, 127372776, 56553546, 14035176, 1542936, 2132316, 306, 97044487, 36858262, 33765157, 2852707, 181908998, 3513398, 20674478, 9637433, 4962128, 2743553, 277928, 527828, 398, 185860809, 39864624, 283623130, 37208185, 9409000, 1568230, 11980, 2110, 75738251, 46189466, 16796201, 3110471, 38981, 5531, 169996332, 47048067, 42709722, 3580272, 1649802, 21192, 315161293, 121746268, 22589323, 7393753, 627583, 78253, 38588414, 160137029, 20703644, 826274, 235004, 224234]}, 'Perm': {'d': 27, 'gens': [806638059760198036614658940, 435557187109449513781389661]}}, 'schur_multiplier': [2, 6], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 8, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^9.C_2^4.C_6', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• ['group_order', 'group_counter'] [1889568, 218] does not appear in gps_conj_classes
• group 1889568.ij does not appear in gps_qchar
• group 1889568.ij does not appear in gps_char
• 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: 158782998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 1889568, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1889568.ij.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1889568.ij', 'subgroup_hash': 2174946664390704901, 'subgroup_order': 1889568, 'subgroup_tex': 'C_3^9.C_2^4.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 158783009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 944784, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '944784.gr', 'subgroup_hash': 4501786173438524635, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^7.C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 158783020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 629856, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.3.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5601133791491910410, 'subgroup_order': 629856, 'subgroup_tex': 'C_3^8.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 158783024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 314928, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.3.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '629856.gq', 'subgroup_hash': 6945368928060937545, 'subgroup_order': 629856, 'subgroup_tex': 'C_3^8.C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 158783025
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 157464, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.4.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.ck', 'subgroup_hash': 1715181047552568615, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^8.(S_3\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 158783026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 314928, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4877498387760485625, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^9.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 158783027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 314928, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': '314928.ip', 'subgroup_hash': 3365147570639039399, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^2\\wr C_2^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 158783028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 157464, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 2670968021992666517, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^9.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 158783029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 1695760410084877973, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^9.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 158782999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 104976, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '314928.iq', 'subgroup_hash': 2115539279105169661, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^2\\wr C_2^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 158783000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7663145386148328555, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^7.C_6^2.C_3', 'supersolvable': False, 'sylow': 0}
  • id: 158783001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.fc', 'subgroup_hash': 1444428931506182356, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^3.C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 158783002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.fc', 'subgroup_hash': 1444428931506182356, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^3.C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 158783003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 157464, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8849996783215151922, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^9.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 158783004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 104976, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 138310753697800881, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^8.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 158783005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 78732, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3412454645336214828, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^9.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 158783006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1889568.ij.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6193664904592433400, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^9.C_3', 'supersolvable': True, 'sylow': 3}
  • id: 158783007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 34992, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.54.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6585073234588995218, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^7.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 158783008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 26244, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.72.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.44', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 44, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '26244.mk', 'subgroup_hash': 2871648462904200151, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 158783010
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 19683, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.96.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.70', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 70, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:A_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5585183472077698458, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^9', 'supersolvable': True, 'sylow': 0}
  • id: 158783011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 11664, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.162.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '162.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 158783012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 8748, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.216.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '216.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.99', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 99, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.na', 'subgroup_hash': 7637982768846944268, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^7:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 158783013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 6561, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.288.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.411', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 411, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2\\times D_6):A_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.1396077', 'subgroup_hash': 7374565384238773860, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^8', 'supersolvable': True, 'sylow': 0}
  • id: 158783014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 2916, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.648.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '648.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.294', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 294, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_3\\times C_6^2):C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ld', 'subgroup_hash': 2310896937790502961, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 158783015
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 27, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.729.A', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '729.a1.M', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2592.go', 'subgroup_hash': 929290681673135987, 'subgroup_order': 2592, 'subgroup_tex': '(C_2\\times C_6^3):C_6', 'supersolvable': False, 'sylow': 0}
  • id: 158783016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 2187, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.864.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '864.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '864.736', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 736, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2^2\\times C_6^2):C_6', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C6'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
  • id: 158783017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 729, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.2592.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2592.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2592.go', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 929290681673135987, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2592, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2\\times C_6^3):C_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C7'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
  • id: 158783018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1889568.ij.59049.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '59049.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 59049, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 2}
  • id: 158783019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 314928, 'characteristic': True, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.69984.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '69984.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '69984.h', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4814747757799365679, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 69984, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^6:C_2^3:A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 158783021
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 314928, 'characteristic': True, 'core_order': 9, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1889568.ij.209952.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '209952.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '209952.y', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8313924744156575404, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 209952, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^7.C_2^3:A_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 158783022
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': False, 'central_factor': False, 'centralizer_order': 944784, 'characteristic': True, 'core_order': 3, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1889568.ij.629856.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '629856.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '629856.gq', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6945368928060937545, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 629856, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^8.C_2^3:A_4', '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: 158783023
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1889568.ij', 'ambient_counter': 218, 'ambient_order': 1889568, 'ambient_tex': 'C_3^9.C_2^4.C_6', 'central': True, 'central_factor': False, 'centralizer_order': 1889568, 'characteristic': True, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 1, 'label': '1889568.ij.1889568.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1889568.a1.N', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1889568.ij', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2174946664390704901, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1889568, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^9.C_2^4.C_6', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D3', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

  Column	Type
  ambient	text
  aut_centralizer_order	numeric
  aut_label	text
  aut_quo_index	numeric
  aut_stab_index	numeric
  aut_weyl_group	text
  aut_weyl_index	numeric
  centralizer	text
  complements	text[]
  conjugacy_class_count	numeric
  contained_in	text[]
  contains	text[]
  core	text
  coset_action_label	text
  count	numeric
  diagramx	smallint[]
  generators	numeric[]
  label	text
  mobius_quo	bigint
  mobius_sub	bigint
  normal_closure	text
  normal_contained_in	text[]
  normal_contains	text[]
  normalizer	text
  old_label	text
  projective_image	text
  quotient_action_image	text
  quotient_action_kernel	text
  quotient_action_kernel_order	numeric
  quotient_fusion	jsonb
  short_label	text
  subgroup_fusion	integer[]
  weyl_group	text

  
  
  • id: 158783017
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '2592.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [65816779612776192000, 7078269219427544608513612800, 206152269067392232593254400, 4474755040154931442310400, 4379214126757202391859200, 3749720079757753221120000], 'label': '1889568.ij.2592.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2592.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2592.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2592.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783018
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '59049.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1889568.a1', 'coset_action_label': None, 'count': 19683, 'diagramx': None, 'generators': [1785082289010909929368876800, 179520363329067368555270400, 5262213065491342627713446400, 3749772137836366791072000, 1631942488743439808526334835], 'label': '1889568.ij.59049.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '59049.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '59049.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783019
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '69984.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '69984.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [19008, 3750, 145359], 'label': '1889568.ij.69984.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '69984.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '69984.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '69984.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158782998
    {'ambient': '1889568.ij', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1101650452903123859, 14725885826019935090, 206152269067392232593254400, 1679077320420833999194176796, 4370181632011052379576064, 3749720079757753221120000, 418837669254600312547540481, 65816779612776192000, 78833448509487802884233432, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158782999
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.A', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [129545, 14725885826019935090, 206152269067392232593254400, 344211, 3749720079757753221120000, 1679077320420833999194174611, 4370181632011052379576781, 65816779612776192000, 4474755040154931442310400, 4379214126757202391859200, 418837669254600312547525289, 78833448509487802884230400, 7078269219427544608513612800], 'label': '1889568.ij.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '6.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783000
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '8.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [206152269067392232593254400, 80694771574190303677925581, 3749720079757753221120000, 418837669254600312547540481, 65816779612776192000, 4474755040154931442310400, 145359, 19008, 1818689794145400085851459609, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.8.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '8.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783001
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '8.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [14725885826019935090, 206152269067392232593254400, 4370181632011052379576064, 3749720079757753221120000, 418837669254600312547540481, 65816779612776192000, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.8.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783002
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '8.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [206152269067392232593254400, 3749720079757753221120000, 418837669254600312547540481, 65816779612776192000, 4474755040154931442310400, 145359, 1679077322853669322644160093, 19008, 4379214126757202391859200, 1818689796578367470162305513, 7078269219427544608513612800, 3750], 'label': '1889568.ij.8.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.C', 'old_label': '8.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783003
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '12.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1889568.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1101650452903123859, 14725885826019935090, 206152269067392232593254400, 4370181632011052379576064, 3749720079757753221120000, 65816779612776192000, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.12.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783004
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '18.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [129545, 14725885826019935090, 206152269067392232593254400, 344211, 3749720079757753221120000, 1679077320420833999194174611, 4370181632011052379576781, 65816779612776192000, 4474755040154931442310400, 4379214126757202391859200, 78833448509487802884230400, 7078269219427544608513612800], 'label': '1889568.ij.18.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '18.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783005
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [19008, 7078269219427544608513612800, 4474755040154931442310400, 145359, 65816779612776192000, 4379214126757202391859200, 3750, 3749720079757753221120000, 4370181632011052379576064, 206152269067392232593254400, 14725885826019935090], 'label': '1889568.ij.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783006
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [18290, 143193, 337253748957847712734611, 6288514726603218783099221119, 4456114541537845438166082393, 218115820410322333354736550, 6872227222758842172208918977, 4654768229126345500511572745, 7089917945945197114026907145, 3032], 'label': '1889568.ij.32.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '32.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783007
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '54.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '54.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [78833448509487802884230400, 7078269219427544608513612800, 4474755040154931442310400, 65816779612776192000, 4379214126757202391859200, 14725885826019916800, 1679077320420833999194181776, 3749720079757753221120000, 4370181632011052379596176, 140361, 206152269067392232593254400], 'label': '1889568.ij.54.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '54.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '54.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783008
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '72.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7078269219427544608513612800, 4474755040154931442310400, 65816779612776192000, 4370181632011052379576781, 4379214126757202391859200, 3749720079757753221120000, 129545, 344211, 206152269067392232593254400, 14725885826019935090], 'label': '1889568.ij.72.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '72.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783009
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [14725885826019935090, 206152269067392232593254400, 1679077320420833999194176796, 4370181632011052379576064, 3749720079757753221120000, 418837669254600312547540481, 65816779612776192000, 78833448509487802884233432, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783010
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '96.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [19008, 65816779612776192000, 3750, 7078269219427544608513612800, 145359, 206152269067392232593254400, 4474755040154931442310400, 4379214126757202391859200, 3749720079757753221120000], 'label': '1889568.ij.96.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '96.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783011
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '162.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '162.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [65816779612776192000, 7078269219427544608513612800, 206152269067392232593254400, 14725885826019916800, 4370181632011052379244800, 1679077320420833999193830400, 4474755040154931442310400, 4379214126757202391859200, 78833448509487802884230400, 3749720079757753221120000], 'label': '1889568.ij.162.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '162.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '162.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783012
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '216.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [65816779612776192000, 7078269219427544608513612800, 140361, 206152269067392232593254400, 14725885826019916800, 4370181632011052379596176, 4474755040154931442310400, 4379214126757202391859200, 3749720079757753221120000], 'label': '1889568.ij.216.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '216.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783013
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '288.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [129545, 65816779612776192000, 7078269219427544608513612800, 206152269067392232593254400, 4474755040154931442310400, 4379214126757202391859200, 344211, 3749720079757753221120000], 'label': '1889568.ij.288.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '288.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783014
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '648.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '69984.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '648.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [65816779612776192000, 7078269219427544608513612800, 206152269067392232593254400, 14725885826019916800, 4370181632011052379244800, 4474755040154931442310400, 4379214126757202391859200, 3749720079757753221120000], 'label': '1889568.ij.648.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '648.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '648.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783015
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '729.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '69984.A', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [78824383272622423431075032, 418830874159019478923476481, 19008, 360197970987102815090, 145359, 361184266077949368064, 3750, 1101650452903123859, 1692015007584321291746189596], 'label': '1889568.ij.729.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.A', 'old_label': '729.a1.M', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783016
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '864.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '96.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '864.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [65816779612776192000, 7078269219427544608513612800, 140361, 206152269067392232593254400, 4474755040154931442310400, 4379214126757202391859200, 3749720079757753221120000], 'label': '1889568.ij.864.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '864.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783020
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '3.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '3.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1101650452903123859, 14725885826019935090, 206152269067392232593254400, 1679077320420833999194176796, 4370181632011052379576064, 3749720079757753221120000, 65816779612776192000, 78833448509487802884233432, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.3.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783021
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '209952.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '209952.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [129545, 344211], 'label': '1889568.ij.209952.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '209952.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '209952.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '209952.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783022
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '629856.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '629856.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [140361], 'label': '1889568.ij.629856.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '629856.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '629856.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '629856.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783023
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '1889568.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1889568.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '1889568.ij.1889568.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1889568.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1889568.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1889568.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783024
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '3.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.B', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [129545, 1101650452903123859, 14725885826019935090, 206152269067392232593254400, 344211, 3749720079757753221120000, 1679077320420833999194174611, 4370181632011052379576781, 418837669254600312547540481, 65816779612776192000, 4474755040154931442310400, 4379214126757202391859200, 78833448509487802884230400, 7078269219427544608513612800], 'label': '1889568.ij.3.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '3.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783025
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1101650452903123859, 14725885826019935090, 206152269067392232593254400, 4370181632011052379576064, 3749720079757753221120000, 418837669254600312547540481, 65816779612776192000, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.4.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '4.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783026
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [14725885826019935090, 206152269067392232593254400, 1679077320420833999194176796, 4370181632011052379576064, 3749720079757753221120000, 65816779612776192000, 78833448509487802884233432, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783027
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [129545, 14725885826019935090, 206152269067392232593254400, 344211, 3749720079757753221120000, 1679077320420833999194174611, 4370181632011052379576781, 418837669254600312547540481, 65816779612776192000, 4474755040154931442310400, 4379214126757202391859200, 78833448509487802884230400, 7078269219427544608513612800], 'label': '1889568.ij.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783028
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1101650452903123859, 14725885826019935090, 206152269067392232593254400, 4370181632011052379576064, 3749720079757753221120000, 65816779612776192000, 78833448509487802884233432, 4474755040154931442310400, 145359, 19008, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '6.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 158783029
    {'ambient': '1889568.ij', 'aut_centralizer_order': None, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [14725885826019935090, 206152269067392232593254400, 4370181632011052379576064, 3749720079757753221120000, 65816779612776192000, 78833448509487802884233432, 4474755040154931442310400, 145359, 19008, 1679077321394289136490362719, 4379214126757202391859200, 7078269219427544608513612800, 3750], 'label': '1889568.ij.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '6.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': None}