Abstract group data - 432.520

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 2, 3, 3, 12, 6, 3], 'aut_gens': [[20189134, 32004859, 22023521, 20206118, 16262215, 20438021, 1305911], [20189134, 782163, 26377746, 16225603, 41053625, 7191393, 1305911], [25834994, 32004859, 20206118, 22023521, 26337246, 5741406, 29656017], [29098928, 689175, 22023521, 33839929, 1239572, 26089305, 1305911], [27355766, 17144144, 7307223, 20206118, 33950737, 39336014, 1305911], [2492512, 8374639, 20206118, 28136091, 16262215, 26089305, 1305911], [8092706, 18902489, 42832787, 9863731, 23632259, 12783622, 1305911], [20189134, 18902489, 22023521, 20206118, 16262215, 20438021, 1305911]], 'aut_group': '432.520', 'aut_hash': 520, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 432, 'aut_permdeg': 72, 'aut_perms': [55575407439779946399003919067509480074341849024646174945925587897591177438453020799099139846537792347957, 10702176858838368127771858964961402679665095462879280464093191878499183687181718712586872678822827180043, 32867214233208652126711913072569718497421547172383083840103384006344978235102157040058336966981688483237, 45220971679821825038892228939748489186443268248488768024602646390501451442362452081207723807059577660108, 13548814129488995593687348922586061482053134371466431979643162679244086569377961746867070179875324249805, 60676832691453999795100506521613435786659966781277130140826414222186852902883340189517347132457600829073, 9791473905517437841599544141750357176146316099590674586233783140945514020460472820150895035809170560], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 36, 1, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 18, 1, 1], [4, 36, 1, 1], [6, 18, 1, 1], [6, 72, 1, 1], [8, 54, 1, 2], [12, 36, 1, 3]], 'aut_supersolvable': False, 'aut_tex': '\\He_3:\\SD_{16}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '432.520', 'autcentquo_hash': 520, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_3:\\SD_{16}', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 36, 1], [3, 2, 1], [3, 24, 1], [4, 18, 1], [4, 36, 1], [6, 18, 1], [6, 72, 1], [8, 54, 2], [12, 36, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '432.520', 'commutator_count': 1, 'commutator_label': '108.15', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 520, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 36, 1, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 18, 1, 1], [4, 36, 1, 1], [6, 18, 1, 1], [6, 72, 1, 1], [8, 54, 2, 1], [12, 36, 1, 1], [12, 36, 2, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 144, 'exponent': 24, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2], [6, 1, 2], [12, 1, 1]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '144.182', 'hash': 520, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [4, 2, 3, 3, 12, 6, 3], 'inner_gens': [[20189134, 782163, 26377746, 16225603, 41053625, 7191393, 1305911], [25834994, 32004859, 20206118, 22023521, 26337246, 5741406, 29656017], [38901070, 2447529, 22023521, 5509503, 4548587, 18041215, 1305911], [30677867, 15936914, 35125891, 20206118, 27993288, 1546886, 1305911], [2492512, 8374639, 20206118, 28136091, 16262215, 26089305, 1305911], [21768073, 18902489, 12908038, 39808163, 9961417, 20438021, 1305911], [20189134, 18902489, 22023521, 20206118, 16262215, 20438021, 1305911]], 'inner_hash': 520, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': '\\He_3:\\SD_{16}', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 4], [2, 3], [6, 4], [8, 2], [12, 1]], 'label': '432.520', 'linC_count': 4, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'He3:SD16', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 14, 'number_divisions': 12, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 40, 'number_subgroups': 511, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 45], [3, 26], [4, 54], [6, 90], [8, 108], [12, 108]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 1], [6, 2], [8, 2], [12, 2]], 'representations': {'PC': {'code': 315743925718442161789025476127419366510060295, 'gens': [1, 2, 5, 6, 7], 'pres': [7, -2, -2, -2, -2, -3, 3, -3, 85, 36, 254, 58, 4491, 438, 165, 4037, 7404, 355, 530, 537, 14118, 7069]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [124895238226433067, 41238302028140584]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [20189134, 32004859, 22023521, 20206118, 16262215, 20438021, 1305911]}, 'Perm': {'d': 27, 'gens': [15836702746677418303130425, 15593415493553930535327482, 594568345998959105472690, 108062212610944756771170, 7550102686338507196661760000, 2516538717432998222691201987, 806634631153204606767248884]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\He_3:\\SD_{16}', 'transitive_degree': 27, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 110217753
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 520, 'group_order': 432, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 14408200, 'size': 1}
  • id: 110217759
    {'aut_label': '2A', 'centralizer': '9.a1.a1', 'counter': 2, 'group_counter': 520, 'group_order': 432, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 32737908, 'size': 9}
  • id: 110217760
    {'aut_label': '2B', 'centralizer': '36.d1.a1', 'counter': 3, 'group_counter': 520, 'group_order': 432, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 12525479, 'size': 36}
  • id: 110217761
    {'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 4, 'group_counter': 520, 'group_order': 432, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 1305911, 'size': 2}
  • id: 110217762
    {'aut_label': '3B', 'centralizer': '24.b1.a1', 'counter': 5, 'group_counter': 520, 'group_order': 432, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 4330535, 'size': 24}
  • id: 110217763
    {'aut_label': '4A', 'centralizer': '18.c1.a1', 'counter': 6, 'group_counter': 520, 'group_order': 432, 'label': '4A', 'order': 4, 'powers': [2, 6], 'representative': 4723061, 'size': 18}
  • id: 110217764
    {'aut_label': '4B', 'centralizer': '36.c1.a1', 'counter': 7, 'group_counter': 520, 'group_order': 432, 'label': '4B', 'order': 4, 'powers': [2, 7], 'representative': 38075043, 'size': 36}
  • id: 110217765
    {'aut_label': '6A', 'centralizer': '18.b1.a1', 'counter': 8, 'group_counter': 520, 'group_order': 432, 'label': '6A', 'order': 6, 'powers': [4, 2], 'representative': 4407485, 'size': 18}
  • id: 110217766
    {'aut_label': '6B', 'centralizer': '72.c1.a1', 'counter': 9, 'group_counter': 520, 'group_order': 432, 'label': '6B', 'order': 6, 'powers': [5, 3], 'representative': 24236830, 'size': 72}
  • id: 110217754
    {'aut_label': '8A1', 'centralizer': '54.c1.a1', 'counter': 10, 'group_counter': 520, 'group_order': 432, 'label': '8A1', 'order': 8, 'powers': [6, 10], 'representative': 23555172, 'size': 54}
  • id: 110217755
    {'aut_label': '8A-1', 'centralizer': '54.c1.a1', 'counter': 11, 'group_counter': 520, 'group_order': 432, 'label': '8A-1', 'order': 8, 'powers': [6, 11], 'representative': 42750111, 'size': 54}
  • id: 110217756
    {'aut_label': '12A', 'centralizer': '36.b1.a1', 'counter': 12, 'group_counter': 520, 'group_order': 432, 'label': '12A', 'order': 12, 'powers': [8, 6], 'representative': 29569995, 'size': 36}
  • id: 110217757
    {'aut_label': '12B1', 'centralizer': '36.c1.a1', 'counter': 13, 'group_counter': 520, 'group_order': 432, 'label': '12B1', 'order': 12, 'powers': [8, 7], 'representative': 42052378, 'size': 36}
  • id: 110217758
    {'aut_label': '12B-1', 'centralizer': '36.c1.a1', 'counter': 14, 'group_counter': 520, 'group_order': 432, 'label': '12B-1', 'order': 12, 'powers': [8, 7], 'representative': 23378431, 'size': 36}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 4554528
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4554532
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
  • id: 4554533
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 4554534
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 4554535
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, 0, -2], 'schur_index': 1}
  • id: 4554536
    {'cdim': 2, 'counter': 6, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.2b', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4554537
    {'cdim': 6, 'counter': 7, 'faithful': True, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.6a', 'multiplicity': 1, 'nt': [27, 141], 'qdim': 6, 'qvalues': [6, -2, 0, -3, 0, 2, 2, 1, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 4554538
    {'cdim': 6, 'counter': 8, 'faithful': True, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.6b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 6, 'qvalues': [6, -2, 0, -3, 0, 2, -2, 1, 0, 0, 0, 1, 1, -1], 'schur_index': 1}
  • id: 4554529
    {'cdim': 8, 'counter': 10, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.8a', 'multiplicity': 1, 'nt': [9, 19], 'qdim': 8, 'qvalues': [8, 0, 2, 8, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4554530
    {'cdim': 8, 'counter': 11, 'faithful': False, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.8b', 'multiplicity': 1, 'nt': [18, 68], 'qdim': 8, 'qvalues': [8, 0, -2, 8, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4554539
    {'cdim': 6, 'counter': 9, 'faithful': True, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.6c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -4, 0, -6, 0, -4, 0, 2, 0, 0, 0, 0, 0, 2], 'schur_index': 1}
  • id: 4554531
    {'cdim': 12, 'counter': 12, 'faithful': True, 'group': '432.520', 'group_order': 432, 'image': None, 'label': '432.520.12a', 'multiplicity': 1, 'nt': [27, 141], 'qdim': 12, 'qvalues': [12, 4, 0, -6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 7125212
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 432, 'label': '432.520.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7125218
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 216, 'label': '432.520.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 7125219
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 216, 'label': '432.520.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7125220
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 216, 'label': '432.520.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 7125221
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 108, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 54, 'label': '432.520.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]]]}
  • id: 7125222
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 54, 'counter': 6, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 27, 'label': '432.520.2b1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7125223
    {'center': '8.a1.a1', 'center_index': 8, 'center_order': 54, 'counter': 7, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1.a1', 'kernel_order': 27, 'label': '432.520.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7125224
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 1, 'dim': 6, 'faithful': True, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '432.520', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.520.6a', 'nt': [27, 141], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 7125225
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 1, 'dim': 6, 'faithful': True, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '432.520', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.520.6b', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 7125213
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '432.520', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.520.6c1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]]]}
  • id: 7125214
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 3, 'dim': 6, 'faithful': True, 'field': [1, -1, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '432.520', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.520.6c2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]]]}
  • id: 7125215
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 3, 'counter': 12, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 3, 'label': '432.520.8a', 'nt': [9, 19], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7125216
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 3, 'counter': 13, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 3, 'label': '432.520.8b', 'nt': [18, 68], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7125217
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '432.520', 'group_counter': 520, 'group_order': 432, 'image': None, 'image_isoclass': '432.520', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.520.12a', 'nt': [27, 141], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 66564963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 432, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '432.520.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.520', 'subgroup_hash': 520, 'subgroup_order': 432, 'subgroup_tex': '\\He_3:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 66564974
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 216, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.520.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.87', 'subgroup_hash': 87, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 66564985
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 216, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.520.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.88', 'subgroup_hash': 88, 'subgroup_order': 216, 'subgroup_tex': '\\SU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 66564996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 216, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.520.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.86', 'subgroup_hash': 86, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 66564998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 108, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.520.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66564999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.17', 'subgroup_hash': 17, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66565000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 66565001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 54, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.520.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66565002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66564964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.17', 'subgroup_hash': 17, 'subgroup_order': 48, 'subgroup_tex': 'Q_8:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66564966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 27, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '432.520.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L3', 'D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 66564967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66564968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66564969
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66564970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '432.520.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 2}
  • id: 66564975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66564976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66564977
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 66564978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 66564979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 66564980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 66564981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 66564982
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 66564983
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66564984
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 66564987
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564988
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.520.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 66564990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66564991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 66564992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 3, 'counter': 36, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '432.520.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.182', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 182, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_9:C_2', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'S', 'D3', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564993
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 66564994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66564995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.520.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 66564997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.520', 'ambient_counter': 520, 'ambient_order': 432, 'ambient_tex': '\\He_3:\\SD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '432.520.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '432.520', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 520, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D4', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 66564983
    {'ambient': '432.520', 'aut_centralizer_order': 24, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '18.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1'], 'contains': ['144.a1.a1', '216.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5672, -1, 5701, -1, 5937, -1, 5943, -1], 'generators': [1305911, 33540391], 'label': '432.520.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564963
    {'ambient': '432.520', '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': '432.a1.a1', 'complements': ['432.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7957, 4231, 7135, 5599, 7237, 3667, 7234, 6362], 'generators': [20189134, 30978591, 32004859, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.520'}
  • id: 66564964
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.8', 'aut_weyl_index': 18, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '27.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9540, -1, 9728, -1, 8355, -1, 8353, -1], 'generators': [20189134, 12783622, 30978591, 32004859, 1305911], 'label': '432.520.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 66564965
    {'ambient': '432.520', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 12, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '36.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2368, -1, 2795, -1, 3337, -1, 3330, -1], 'generators': [32004859, 1305911, 33540391, 3123314], 'label': '432.520.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 66564966
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1'], 'contains': ['48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3862, 4231, 4582, 5599, 1651, 3667, 1652, 6362], 'generators': [1305911, 8534127, 3123314], 'label': '432.520.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.520', 'quotient_action_image': '16.8', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 66564967
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.8', 'aut_weyl_index': 18, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '54.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6652, -1, 6055, -1, 5917, -1, 5912, -1], 'generators': [12783622, 30978591, 32004859, 1305911], 'label': '432.520.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
  • id: 66564968
    {'ambient': '432.520', 'aut_centralizer_order': 6, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 54, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '54.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8411, -1, 9404, -1, 7460, -1, 7458, -1], 'generators': [20189134, 12783622, 30978591, 1305911], 'label': '432.520.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66564969
    {'ambient': '432.520', 'aut_centralizer_order': 4, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9639, -1, 8244, -1, 9624, -1, 9624, -1], 'generators': [12783622, 33744134, 30978591, 1305911], 'label': '432.520.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66564970
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4555, -1, 4520, -1, 4373, -1, 4377, -1], 'generators': [1305911, 33540391, 3123314], 'label': '432.520.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66564971
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '72.c1.a1', '72.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1479, -1, 676, -1, 594, -1, 595, -1], 'generators': [32004859, 1305911, 8534127], 'label': '432.520.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66564972
    {'ambient': '432.520', 'aut_centralizer_order': 1, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '72.d1.a1', '72.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [361, -1, 1816, -1, 2483, -1, 2486, -1], 'generators': [32004859, 1305911, 3123314], 'label': '432.520.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 66564973
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.3', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': '27T141', 'count': 27, 'diagramx': [9322, -1, 9465, -1, 8659, -1, 8657, -1], 'generators': [20189134, 28011675, 30978591, 32004859], 'label': '432.520.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66564974
    {'ambient': '432.520', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.520', 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '18.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5682, 8779, 5267, 2105, 5398, 7609, 5394, 2391], 'generators': [30978591, 32004859, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.520'}
  • id: 66564975
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.a1.a1'], 'contains': ['72.a1.a1', '72.d1.a1', '108.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4990, -1, 5076, -1, 5429, -1, 5435, -1], 'generators': [32004859, 1305911, 33540391], 'label': '432.520.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66564976
    {'ambient': '432.520', 'aut_centralizer_order': 12, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '108.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7749, -1, 6822, -1, 7867, -1, 7875, -1], 'generators': [12783622, 30978591, 1305911], 'label': '432.520.36.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 66564977
    {'ambient': '432.520', 'aut_centralizer_order': 12, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '108.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6275, -1, 7720, -1, 6242, -1, 6248, -1], 'generators': [20189134, 12783622, 1305911], 'label': '432.520.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564978
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.e1.a1', '108.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': '36T704', 'count': 36, 'diagramx': [2022, -1, 1948, -1, 3316, -1, 3320, -1], 'generators': [32004859, 33540391, 30922296], 'label': '432.520.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '36.d1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66564979
    {'ambient': '432.520', 'aut_centralizer_order': 9, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['144.a1.a1', '144.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3516, -1, 3532, -1, 2128, -1, 2130, -1], 'generators': [1305911, 3123314], 'label': '432.520.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 66564980
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.3', 'aut_weyl_index': 54, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7284, -1, 6994, -1, 7054, -1, 7061, -1], 'generators': [28011675, 30978591, 32004859], 'label': '432.520.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66564981
    {'ambient': '432.520', 'aut_centralizer_order': 6, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 54, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8491, -1, 9465, -1, 8679, -1, 8688, -1], 'generators': [20189134, 28011675, 30978591], 'label': '432.520.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 66564982
    {'ambient': '432.520', 'aut_centralizer_order': 8, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '54.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '27.a1.a1'], 'contains': ['108.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9619, -1, 8527, -1, 9411, -1, 9420, -1], 'generators': [28011675, 33744134, 30978591], 'label': '432.520.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564984
    {'ambient': '432.520', 'aut_centralizer_order': 6, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.a1'], 'contains': ['144.b1.a1', '216.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3526, -1, 2846, -1, 4373, -1, 4377, -1], 'generators': [33540391, 30922296], 'label': '432.520.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66564985
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': ['216.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '18.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7512, 4231, 7588, 7895, 6780, 3667, 6777, 8971], 'generators': [20189134, 30978591, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '432.520', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 66564986
    {'ambient': '432.520', 'aut_centralizer_order': 6, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.d1.a1'], 'contains': ['144.b1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1548, -1, 272, -1, 1346, -1, 1347, -1], 'generators': [32004859, 23762183], 'label': '432.520.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '72.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564987
    {'ambient': '432.520', 'aut_centralizer_order': 6, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '36.a1.a1'], 'contains': ['144.a1.a1', '216.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2260, -1, 1736, -1, 3641, -1, 3645, -1], 'generators': [32004859, 1305911], 'label': '432.520.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66564988
    {'ambient': '432.520', 'aut_centralizer_order': 2, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.d1.a1'], 'contains': ['144.b1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [836, -1, 1009, -1, 2910, -1, 2913, -1], 'generators': [32004859, 3123314], 'label': '432.520.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '72.e1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 66564989
    {'ambient': '432.520', 'aut_centralizer_order': 4, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1', '54.a1.a1'], 'contains': ['216.a1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5346, -1, 5137, -1, 5155, -1, 5160, -1], 'generators': [32004859, 33540391], 'label': '432.520.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564990
    {'ambient': '432.520', 'aut_centralizer_order': 24, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7948, -1, 7398, -1, 7867, -1, 7875, -1], 'generators': [28011675, 30978591], 'label': '432.520.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564991
    {'ambient': '432.520', 'aut_centralizer_order': 12, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '54.b1.a1'], 'contains': ['216.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6740, -1, 8124, -1, 6668, -1, 6675, -1], 'generators': [20189134, 28011675], 'label': '432.520.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '108.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564992
    {'ambient': '432.520', 'aut_centralizer_order': 216, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.a1.a1', '72.d1.a1'], 'contains': ['432.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3823, 4231, 3330, 5599, 4007, 3667, 4011, 6362], 'generators': [1305911], 'label': '432.520.144.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.520', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.41', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564993
    {'ambient': '432.520', 'aut_centralizer_order': 18, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.b1.a1', '72.c1.a1', '72.e1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3091, -1, 2341, -1, 2544, -1, 2547, -1], 'generators': [3123314], 'label': '432.520.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 66564994
    {'ambient': '432.520', 'aut_centralizer_order': 48, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5702, -1, 5500, -1, 5541, -1, 5546, -1], 'generators': [33540391], 'label': '432.520.216.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66564995
    {'ambient': '432.520', 'aut_centralizer_order': 12, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 432, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.d1.a1', '72.e1.a1', '108.a1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1963, -1, 1786, -1, 3276, -1, 3279, -1], 'generators': [32004859], 'label': '432.520.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '216.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66564996
    {'ambient': '432.520', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.520', 'aut_weyl_index': 1, 'centralizer': '432.a1.a1', 'complements': ['216.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '18.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8402, 1221, 6681, 5599, 7694, 1058, 7692, 6362], 'generators': [33744134, 30978591, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '432.520', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.520'}
  • id: 66564997
    {'ambient': '432.520', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '216.a1.a1', '216.b1.a1'], 'contains': [], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3536, 4231, 2785, 5599, 3641, 3667, 3645, 6362], 'generators': [], 'label': '432.520.432.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 66564998
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '36.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7512, 4231, 6146, 5599, 6546, 3667, 6543, 6362], 'generators': [30978591, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 66564999
    {'ambient': '432.520', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.87', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '12.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4070, -1, 3300, -1, 3377, -1, 3371, -1], 'generators': [32004859, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.87'}
  • id: 66565000
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.41', 'aut_weyl_index': 6, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '36.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6098, -1, 7588, -1, 4698, -1, 4692, -1], 'generators': [20189134, 1305911, 33540391, 8534127, 3123314], 'label': '432.520.4.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.c1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 66565001
    {'ambient': '432.520', 'aut_centralizer_order': 3, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4555, 4231, 4763, 5599, 4373, 3667, 4377, 6362], 'generators': [1305911, 33540391, 8534127, 3123314], 'label': '432.520.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
  • id: 66565002
    {'ambient': '432.520', 'aut_centralizer_order': 1, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2101, -1, 1725, -1, 2047, -1, 2039, -1], 'generators': [32004859, 1305911, 8534127, 3123314], 'label': '432.520.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '432.520', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}