Abstract subgroup data - 3201186852864000.a.205632.a1.a1

Formats: - HTML - YAML - JSON - 2025-09-09T07:35:18.832771

• 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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3201186852864000.a', 'ambient_counter': 1, 'ambient_order': 3201186852864000, 'ambient_tex': 'A_{18}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3201186852864000.a.205632.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '205632.A', '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': 205632, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 15567552000, 'subgroup_tex': 'C_5.A_{13}', 'supersolvable': False, 'sylow': 0}
• 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

  
  {'ambient': '3201186852864000.a', 'aut_centralizer_order': None, 'aut_label': '205632.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': None, 'coset_action_label': None, 'count': 51408, 'diagramx': None, 'generators': [107, 4037913, 1485605260339200, 379225566720012, 83871513, 1067149462579835, 379225566720800, 776845753171350, 11390, 248009, 776845753585473, 480, 1067149462579204, 518918400, 379225566720082], 'label': '3201186852864000.a.205632.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '205632.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '205632.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
• label None does not appear in gps_groups
• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': False, 'almost_simple': True, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[357089030732313, 376610217984000], [357089030732313, 1068369958656000], [1110309466700313, 376610217984000], [1046327350936624, 752006689868313], [370259702679545, 691853668940313], [3463097423839865, 19709043425433], [357109228636624, 376610217984000], [363721355882012, 503548559539200], [365403679134160, 524471349790080], [357862470682451, 376610217984000], [358274595004381, 376610217984000], [357091134662192, 376610217984000], [357093123104554, 376610217984000], [357089032329107, 376610217984000], [357089057205253, 376610217984000], [357089065432531, 376610217984000], [357089030988655, 376610217984000], [357089030738152, 376610217984000], [357089030756569, 376610217984000], [357089030735864, 376610217984000], [357089030743031, 376610217984000], [357089030732540, 376610217984000], [357089030751908, 376610217984000], [357089030732723, 376610217984000], [357089030732326, 376610217984000], [588641322247936, 1052889471515]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 6402373705728000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 9180, 1, 1], [2, 4594590, 1, 1], [2, 192972780, 1, 1], [2, 310134825, 1, 1], [3, 1632, 1, 1], [3, 742560, 1, 1], [3, 108908800, 1, 1], [3, 4574169600, 1, 1], [3, 12197785600, 1, 1], [3, 36593356800, 1, 1], [4, 1670760, 1, 1], [4, 55135080, 1, 1], [4, 827026200, 1, 1], [4, 2481078600, 1, 1], [4, 17367550200, 1, 1], [4, 34735100400, 1, 1], [4, 260513253000, 1, 1], [4, 347351004000, 1, 2], [4, 521026506000, 1, 1], [5, 205632, 1, 1], [5, 3175780608, 1, 1], [5, 1422749712384, 1, 1], [6, 6683040, 1, 1], [6, 147026880, 1, 1], [6, 1102701600, 1, 2], [6, 7718911200, 1, 2], [6, 30875644800, 1, 1], [6, 35286451200, 1, 1], [6, 38594556000, 1, 1], [6, 41167526400, 1, 1], [6, 102918816000, 1, 1], [6, 123502579200, 1, 1], [6, 138940401600, 1, 1], [6, 205837632000, 1, 1], [6, 1235025792000, 1, 3], [6, 3293402112000, 1, 1], [6, 4940103168000, 1, 2], [6, 5557616064000, 1, 1], [7, 22913280, 1, 1], [7, 2722097664000, 1, 1], [8, 9924314400, 1, 1], [8, 208410602400, 1, 1], [8, 277880803200, 1, 1], [8, 694702008000, 1, 1], [8, 12504636144000, 1, 2], [8, 25009272288000, 1, 1], [9, 1960358400, 1, 1], [9, 329340211200, 1, 1], [9, 4391202816000, 1, 1], [9, 6586804224000, 1, 1], [9, 39520825344000, 1, 1], [10, 441080640, 1, 1], [10, 27788080320, 1, 2], [10, 333456963840, 1, 1], [10, 444609285120, 1, 1], [10, 666913927680, 1, 1], [10, 6669139276800, 1, 1], [10, 64023737057280, 1, 1], [11, 115482931200, 1, 1], [12, 735134400, 1, 1], [12, 6616209600, 1, 1], [12, 13232419200, 1, 1], [12, 61751289600, 1, 1], [12, 92626934400, 1, 1], [12, 138940401600, 1, 1], [12, 411675264000, 1, 1], [12, 463134672000, 1, 1], [12, 694702008000, 1, 1], [12, 741015475200, 1, 1], [12, 823350528000, 1, 1], [12, 926269344000, 1, 1], [12, 1235025792000, 1, 1], [12, 1389404016000, 1, 3], [12, 2778808032000, 1, 2], [12, 7410154752000, 1, 1], [12, 8336424096000, 1, 1], [12, 11115232128000, 1, 4], [12, 66691392768000, 1, 1], [12, 88921857024000, 1, 2], [13, 4104085708800, 1, 1], [14, 22684147200, 1, 1], [14, 396972576000, 1, 1], [14, 8166292992000, 1, 1], [14, 114328101888000, 1, 1], [15, 117621504, 1, 1], [15, 14114580480, 1, 1], [15, 329340211200, 1, 1], [15, 355687428096, 1, 1], [15, 658680422400, 1, 1], [15, 2845499424768, 1, 1], [15, 3556874280960, 1, 1], [15, 71137485619200, 1, 1], [15, 71137485619200, 2, 1], [16, 200074178304000, 1, 1], [17, 188305108992000, 2, 1], [18, 741015475200, 1, 1], [18, 1852538688000, 1, 1], [18, 14820309504000, 1, 1], [18, 59281238016000, 1, 1], [20, 31757806080, 1, 1], [20, 333456963840, 1, 1], [20, 1111523212800, 1, 1], [20, 4001483566080, 1, 1], [20, 5001854457600, 1, 1], [20, 6669139276800, 1, 1], [20, 8002967132160, 1, 1], [20, 20007417830400, 1, 1], [21, 7561382400, 1, 1], [21, 423437414400, 1, 1], [21, 2822916096000, 1, 1], [21, 21776781312000, 1, 1], [22, 12125707776000, 1, 1], [24, 1111523212800, 1, 1], [24, 5557616064000, 1, 2], [24, 11115232128000, 1, 3], [24, 16672848192000, 1, 1], [24, 44460928512000, 1, 1], [26, 61561285632000, 1, 1], [28, 952734182400, 1, 1], [28, 4763670912000, 1, 2], [28, 114328101888000, 1, 1], [30, 74101547520, 1, 1], [30, 555761606400, 1, 1], [30, 889218570240, 1, 1], [30, 988020633600, 1, 1], [30, 1482030950400, 1, 1], [30, 4446092851200, 1, 1], [30, 5335311421440, 1, 1], [30, 10670622842880, 1, 1], [30, 17784371404800, 1, 4], [30, 53353114214400, 1, 1], [33, 8083805184000, 1, 1], [33, 32335220736000, 1, 1], [35, 254062448640, 1, 1], [35, 18292496302080, 1, 1], [36, 14820309504000, 1, 1], [36, 22230464256000, 1, 1], [36, 29640619008000, 1, 1], [39, 82081714176000, 1, 1], [40, 13338278553600, 1, 1], [40, 40014835660800, 1, 1], [40, 80029671321600, 1, 1], [42, 793945152000, 1, 1], [42, 1587890304000, 1, 1], [42, 6351561216000, 1, 1], [42, 12703122432000, 1, 1], [42, 25406244864000, 1, 1], [44, 72754246656000, 1, 1], [45, 5928123801600, 1, 1], [45, 23712495206400, 2, 1], [55, 58203397324800, 1, 1], [56, 57164050944000, 1, 1], [60, 2223046425600, 1, 2], [60, 6669139276800, 1, 1], [60, 8892185702400, 1, 2], [60, 17784371404800, 1, 1], [60, 53353114214400, 1, 1], [63, 50812489728000, 1, 1], [65, 49249028505600, 2, 1], [66, 24251415552000, 1, 1], [70, 11432810188800, 1, 1], [77, 41573855232000, 2, 1], [84, 9527341824000, 1, 1], [84, 19054683648000, 1, 1], [84, 38109367296000, 1, 1], [90, 17784371404800, 1, 1], [105, 10162497945600, 1, 2], [120, 26676557107200, 1, 1], [140, 22865620377600, 1, 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, 9180, 1], [2, 4594590, 1], [2, 192972780, 1], [2, 310134825, 1], [3, 1632, 1], [3, 742560, 1], [3, 108908800, 1], [3, 4574169600, 1], [3, 12197785600, 1], [3, 36593356800, 1], [4, 1670760, 1], [4, 55135080, 1], [4, 827026200, 1], [4, 2481078600, 1], [4, 17367550200, 1], [4, 34735100400, 1], [4, 260513253000, 1], [4, 347351004000, 2], [4, 521026506000, 1], [5, 205632, 1], [5, 3175780608, 1], [5, 1422749712384, 1], [6, 6683040, 1], [6, 147026880, 1], [6, 1102701600, 2], [6, 7718911200, 2], [6, 30875644800, 1], [6, 35286451200, 1], [6, 38594556000, 1], [6, 41167526400, 1], [6, 102918816000, 1], [6, 123502579200, 1], [6, 138940401600, 1], [6, 205837632000, 1], [6, 1235025792000, 3], [6, 3293402112000, 1], [6, 4940103168000, 2], [6, 5557616064000, 1], [7, 22913280, 1], [7, 2722097664000, 1], [8, 9924314400, 1], [8, 208410602400, 1], [8, 277880803200, 1], [8, 694702008000, 1], [8, 12504636144000, 2], [8, 25009272288000, 1], [9, 1960358400, 1], [9, 329340211200, 1], [9, 4391202816000, 1], [9, 6586804224000, 1], [9, 39520825344000, 1], [10, 441080640, 1], [10, 27788080320, 2], [10, 333456963840, 1], [10, 444609285120, 1], [10, 666913927680, 1], [10, 6669139276800, 1], [10, 64023737057280, 1], [11, 115482931200, 1], [12, 735134400, 1], [12, 6616209600, 1], [12, 13232419200, 1], [12, 61751289600, 1], [12, 92626934400, 1], [12, 138940401600, 1], [12, 411675264000, 1], [12, 463134672000, 1], [12, 694702008000, 1], [12, 741015475200, 1], [12, 823350528000, 1], [12, 926269344000, 1], [12, 1235025792000, 1], [12, 1389404016000, 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