Abstract subgroup data - 3201186852864000.a.73440.a1.a1

Formats: - HTML - YAML - JSON - 2025-09-15T03:20:09.196114

• 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': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3201186852864000.a.73440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '73440.A', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 73440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '43589145600.a', 'subgroup_hash': None, 'subgroup_order': 43589145600, 'subgroup_tex': 'A_{14}', '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': '73440.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': 3060, 'diagramx': None, 'generators': [12976997913, 13499954224], 'label': '3201186852864000.a.73440.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '73440.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '73440.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
• 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': [[6270975513, 6706022400], [6270975513, 18720979200], [19683020313, 6706022400], [47074008393, 43633099440], [16773131529, 13216498680], [6434609889, 10102988280], [45437321159, 5273055512], [6271284629, 6706022400], [6270975596, 6706022400], [6272392960, 6706022400], [6273729881, 6706022400], [65926975412, 4833969990], [6666289063, 7707571200], [6284846010, 6706022400], [6299702580, 6706022400], [6305563099, 6706022400], [6296087407, 6706022400], [6271004764, 6706022400], [6270975839, 6706022400], [6270976076, 6706022400], [6270975526, 6706022400], [78149416687, 25810584]], 'aut_group': '87178291200.a', 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 87178291200, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 3003, 1, 1], [2, 315315, 1, 1], [2, 945945, 1, 1], [3, 728, 1, 1], [3, 120120, 1, 1], [3, 4484480, 1, 1], [3, 22422400, 1, 1], [4, 270270, 1, 1], [4, 3783780, 1, 1], [4, 5675670, 1, 1], [4, 18918900, 1, 1], [4, 113513400, 1, 1], [4, 170270100, 1, 1], [5, 48048, 1, 1], [5, 72648576, 1, 1], [6, 720720, 1, 1], [6, 10090080, 1, 1], [6, 12612600, 1, 2], [6, 25225200, 1, 1], [6, 67267200, 1, 1], [6, 151351200, 1, 1], [6, 403603200, 1, 2], [6, 605404800, 1, 1], [7, 2471040, 1, 1], [7, 889574400, 1, 1], [8, 227026800, 1, 2], [8, 1362160800, 1, 1], [9, 80720640, 1, 1], [9, 1614412800, 1, 1], [10, 18162144, 1, 1], [10, 45405360, 1, 1], [10, 217945728, 1, 1], [10, 2179457280, 1, 1], [11, 1320883200, 1, 1], [12, 30270240, 1, 1], [12, 151351200, 1, 4], [12, 302702400, 1, 1], [12, 454053600, 1, 1], [12, 1210809600, 1, 1], [12, 3632428800, 1, 1], [13, 3353011200, 2, 1], [14, 259459200, 1, 1], [15, 8072064, 1, 1], [15, 107627520, 1, 1], [15, 161441280, 1, 1], [15, 581188608, 1, 1], [18, 1210809600, 1, 1], [20, 363242880, 1, 1], [20, 544864320, 1, 1], [20, 2179457280, 1, 1], [21, 172972800, 1, 1], [21, 691891200, 1, 1], [24, 1816214400, 1, 2], [28, 1556755200, 1, 1], [30, 363242880, 1, 1], [30, 1452971520, 1, 1], [33, 1320883200, 2, 1], [35, 1245404160, 1, 1], [42, 518918400, 1, 1], [45, 968647680, 2, 1], [60, 726485760, 1, 1]], 'aut_supersolvable': None, 'aut_tex': 'S_{14}', '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, 3003, 1], [2, 315315, 1], [2, 945945, 1], [3, 728, 1], [3, 120120, 1], [3, 4484480, 1], [3, 22422400, 1], [4, 270270, 1], [4, 3783780, 1], [4, 5675670, 1], [4, 18918900, 1], [4, 113513400, 1], [4, 170270100, 1], [5, 48048, 1], [5, 72648576, 1], [6, 720720, 1], [6, 10090080, 1], [6, 12612600, 2], [6, 25225200, 1], [6, 67267200, 1], [6, 151351200, 1], [6, 403603200, 2], [6, 605404800, 1], [7, 2471040, 1], [7, 889574400, 1], [8, 227026800, 2], [8, 1362160800, 1], [9, 80720640, 1], [9, 1614412800, 1], [10, 18162144, 1], [10, 45405360, 1], [10, 217945728, 1], [10, 2179457280, 1], [11, 1320883200, 1], [12, 30270240, 1], [12, 151351200, 4], [12, 302702400, 1], [12, 454053600, 1], [12, 1210809600, 1], [12, 3632428800, 1], [13, 3353011200, 2], [14, 259459200, 1], [15, 8072064, 1], [15, 107627520, 1], [15, 161441280, 1], [15, 581188608, 1], [18, 1210809600, 1], [20, 363242880, 1], [20, 544864320, 1], [20, 2179457280, 1], [21, 172972800, 1], [21, 691891200, 1], [24, 1816214400, 2], [28, 1556755200, 1], [30, 363242880, 1], [30, 1452971520, 1], [33, 1320883200, 2], [35, 1245404160, 1], [42, 518918400, 1], [45, 968647680, 2], [60, 726485760, 1]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '43589145600.a', 'commutator_count': 1, 'commutator_label': '43589145600.a', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['43589145600.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3003, 1, 1], [2, 315315, 1, 1], [2, 945945, 1, 1], [3, 728, 1, 1], [3, 120120, 1, 1], [3, 4484480, 1, 1], [3, 22422400, 1, 1], [4, 270270, 1, 1], [4, 3783780, 1, 1], [4, 5675670, 1, 1], [4, 18918900, 1, 1], [4, 113513400, 1, 1], [4, 170270100, 1, 1], [5, 48048, 1, 1], [5, 72648576, 1, 1], [6, 720720, 1, 1], [6, 10090080, 1, 1], [6, 12612600, 1, 2], [6, 25225200, 1, 1], [6, 67267200, 1, 1], [6, 151351200, 1, 1], [6, 403603200, 1, 2], [6, 605404800, 1, 1], [7, 2471040, 1, 1], [7, 889574400, 1, 1], [8, 227026800, 1, 2], [8, 1362160800, 1, 1], [9, 80720640, 1, 1], [9, 1614412800, 1, 1], [10, 18162144, 1, 1], [10, 45405360, 1, 1], [10, 217945728, 1, 1], [10, 2179457280, 1, 1], [11, 1320883200, 1, 1], [12, 30270240, 1, 1], [12, 151351200, 1, 4], [12, 302702400, 1, 1], [12, 454053600, 1, 1], [12, 1210809600, 1, 1], [12, 3632428800, 1, 1], [13, 3353011200, 2, 1], [14, 259459200, 1, 1], [15, 8072064, 1, 1], [15, 107627520, 1, 1], [15, 161441280, 1, 1], [15, 581188608, 1, 1], [18, 1210809600, 1, 1], [20, 363242880, 1, 1], [20, 544864320, 1, 1], [20, 2179457280, 1, 1], [21, 172972800, 1, 1], [21, 691891200, 1, 1], [24, 1816214400, 1, 2], [28, 1556755200, 1, 1], [30, 363242880, 1, 1], [30, 1452971520, 1, 1], [33, 1320883200, 2, 1], [35, 1245404160, 1, 1], [42, 518918400, 1, 1], [45, 968647680, 2, 1], [60, 726485760, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 360360, 'exponents_of_order': [10, 5, 2, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7, 11, 13], 'factors_of_order': [2, 3, 5, 7, 11, 13], 'faithful_reps': [[13, 1, 1], [77, 1, 1], [78, 1, 1], [273, 1, 1], [286, 1, 1], [429, 1, 1], [560, 1, 1], [637, 1, 1], [715, 1, 1], [1001, 1, 2], [1287, 1, 1], [1365, 1, 1], [1716, 1, 1], [2002, 1, 1], [2079, 1, 1], [4368, 1, 1], [4576, 1, 1], [4752, 1, 2], [4928, 1, 1], [5733, 1, 1], [6006, 1, 3], [6435, 1, 1], [7007, 1, 3], [7644, 1, 1], [8085, 1, 1], [9009, 1, 1], [12012, 1, 2], [13650, 1, 1], [14014, 1, 3], [15015, 1, 3], [15444, 1, 1], [16016, 1, 1], [20384, 1, 1], [21021, 1, 3], [21450, 1, 2], [23296, 1, 1], [24960, 1, 1], [27027, 1, 2], [28028, 1, 1], [28665, 1, 1], [29952, 1, 2], [34320, 1, 2], [35035, 1, 2], [36608, 1, 1], [42042, 1, 2], [47775, 1, 1], [48048, 1, 2], [50050, 1, 1], [63063, 1, 1], [64064, 1, 1], [69498, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '43589145600.a', 'hash': 3155801648195941231, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'A_{14}', 'inner_used': None, 'irrC_degree': 13, 'irrQ_degree': 13, 'irrQ_dim': 13, 'irrR_degree': 13, 'irrep_stats': [[1, 1], [13, 1], [77, 1], [78, 1], [273, 1], [286, 1], [429, 1], [560, 1], [637, 1], [715, 1], [1001, 2], [1287, 1], [1365, 1], [1716, 1], [2002, 1], [2079, 1], [4368, 1], [4576, 1], [4752, 2], [4928, 1], [5733, 1], [6006, 3], [6435, 1], [7007, 3], [7644, 1], [8085, 1], [9009, 1], [12012, 2], [13650, 1], [14014, 3], [15015, 3], [15444, 1], [16016, 1], [20384, 1], [21021, 3], [21450, 2], [23296, 1], [24960, 1], [27027, 2], [28028, 1], [28665, 1], [29952, 2], [34320, 2], [35035, 2], [36608, 1], [42042, 2], [47775, 1], [48048, 2], [50050, 1], [63063, 1], [64064, 1], [69498, 1]], 'label': '43589145600.a', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'A14', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 69, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 72, 'number_divisions': 69, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 43589145600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1264263], [3, 27027728], [4, 312432120], [5, 72696624], [6, 1692490800], [7, 892045440], [8, 1816214400], [9, 1695133440], [10, 2460970512], [11, 1320883200], [12, 6235669440], [13, 6706022400], [14, 259459200], [15, 858329472], [18, 1210809600], [20, 3087564480], [21, 864864000], [24, 3632428800], [28, 1556755200], [30, 1816214400], [33, 2641766400], [35, 1245404160], [42, 518918400], [45, 1937295360], [60, 726485760]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '2.1', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 2, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [13, 1], [77, 1], [78, 1], [273, 1], [286, 1], [429, 1], [560, 1], [637, 1], [715, 1], [1001, 2], [1287, 1], [1365, 1], [1716, 1], [2002, 1], [2079, 1], [4368, 1], [4576, 1], [4928, 1], [5733, 1], [6006, 3], [6435, 1], [7007, 3], [7644, 1], [8085, 1], [9009, 1], [9504, 1], [12012, 2], [13650, 1], [14014, 3], [15015, 3], [15444, 1], [16016, 1], [20384, 1], [21021, 3], [21450, 2], [23296, 1], [24960, 1], [27027, 2], [28028, 1], [28665, 1], [35035, 2], [36608, 1], [42042, 2], [47775, 1], [48048, 2], [50050, 1], [59904, 1], [63063, 1], [64064, 1], [68640, 1], [69498, 1]], 'representations': {'Perm': {'d': 14, 'gens': [6706022400, 6270975513]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 12579840, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_{14}', 'transitive_degree': 14, 'wreath_data': None, 'wreath_product': False}
• 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, 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16672848192000, 1], [24, 44460928512000, 1], [26, 61561285632000, 1], [28, 952734182400, 1], [28, 4763670912000, 2], [28, 114328101888000, 1], [30, 74101547520, 1], [30, 555761606400, 1], [30, 889218570240, 1], [30, 988020633600, 1], [30, 1482030950400, 1], [30, 4446092851200, 1], [30, 5335311421440, 1], [30, 10670622842880, 1], [30, 17784371404800, 4], [30, 53353114214400, 1], [33, 8083805184000, 1], [33, 32335220736000, 1], [35, 254062448640, 1], [35, 18292496302080, 1], [36, 14820309504000, 1], [36, 22230464256000, 1], [36, 29640619008000, 1], [39, 82081714176000, 1], [40, 13338278553600, 1], [40, 40014835660800, 1], [40, 80029671321600, 1], [42, 793945152000, 1], [42, 1587890304000, 1], [42, 6351561216000, 1], [42, 12703122432000, 1], [42, 25406244864000, 1], [44, 72754246656000, 1], [45, 5928123801600, 1], [45, 23712495206400, 2], [55, 58203397324800, 1], [56, 57164050944000, 1], [60, 2223046425600, 2], [60, 6669139276800, 1], [60, 8892185702400, 2], [60, 17784371404800, 1], [60, 53353114214400, 1], [63, 50812489728000, 1], [65, 49249028505600, 2], [66, 24251415552000, 1], [70, 11432810188800, 1], [77, 41573855232000, 2], [84, 9527341824000, 1], [84, 19054683648000, 1], [84, 38109367296000, 1], [90, 17784371404800, 1], [105, 10162497945600, 2], [120, 26676557107200, 1], [140, 22865620377600, 1]], 'center_label': '1.1', 'center_order': None, 'central_product': False, 'central_quotient': '3201186852864000.a', 'commutator_count': 1, 'commutator_label': '3201186852864000.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['3201186852864000.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_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, 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