Abstract group data - 17496.qe

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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': 6, 'aut_exponent': 72, 'aut_gen_orders': [18, 6, 12], 'aut_gens': [[319415830137892143429822074121244263923880, 96033410119514675706661895146131406706161], [233719098912429091953225353441640628168916, 74164207385449231911033949802551703091144], [361361678346716258599724232639961820259812, 329448041381014549978282575152728205001454], [340079155339383808811648475864054919280187, 32212137332606261667161648693985050147250]], 'aut_group': None, 'aut_hash': 815403555457547113, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2519424, 'aut_permdeg': 4374, 'aut_perms': 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'aut_phi_ratio': 432.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [3, 2, 3, 1], [3, 4, 2, 1], [3, 4, 3, 1], [3, 72, 4, 1], [3, 72, 8, 1], [3, 216, 6, 1], [4, 1458, 3, 1], [6, 162, 3, 1], [6, 324, 2, 1], [6, 324, 3, 1], [12, 1458, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_3^4.(Q_8.A_4).D_6', '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': 72, 'autcentquo_group': None, 'autcentquo_hash': 815403555457547113, 'autcentquo_nilpotent': False, 'autcentquo_order': 2519424, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.C_3^4.Q_8.A_4.D_6', 'cc_stats': [[1, 1, 1], [2, 81, 1], [3, 2, 3], [3, 4, 5], [3, 72, 12], [3, 216, 6], [4, 1458, 3], [6, 162, 3], [6, 324, 5], [12, 1458, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '17496.qe', 'commutator_count': 1, 'commutator_label': None, 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 421, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 4, 2, 1], [3, 72, 1, 4], [3, 72, 2, 4], [3, 216, 1, 6], [4, 1458, 1, 3], [6, 162, 1, 3], [6, 324, 1, 3], [6, 324, 2, 1], [12, 1458, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 27, 'exponent': 12, 'exponents_of_order': [7, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4], [24, 0, 8]], 'familial': False, 'frattini_label': '27.5', 'frattini_quotient': '648.730', 'hash': 785846807519522182, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 12], 'inner_gens': [[319415830137892143429822074121244263923880, 361364682783432690502745734246035494597762], [201803017385529329428070213018332206747000, 96033410119514675706661895146131406706161]], 'inner_hash': 785846807519522182, 'inner_nilpotent': False, 'inner_order': 17496, 'inner_split': False, 'inner_tex': 'C_3^5:\\PSU(3,2)', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 1], [8, 10], [12, 4], [18, 12], [24, 8], [36, 6]], 'label': '17496.qe', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^5:PSU(3,2)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 45, 'number_divisions': 36, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 171, 'number_subgroup_classes': 1740, 'number_subgroups': 97318, 'old_label': None, 'order': 17496, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 81], [3, 2186], [4, 4374], [6, 2106], [12, 8748]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 3, 2, 2], 'outer_gen_pows': [106074329806011858637581239161163627802115, 265924437832569770495600816657303717725587, 0, 526279358197957466858071948286135284, 0, 265924964103390288221010011649889716026403], 'outer_gens': [[42250578953931637012348700796297190822464, 106074058644640400656636413118367201347799], [64119518538238680386406394893295156323240, 371992792067617665403555394657963242821571], [319415830137892143429822074121244263923880, 351327022396519661709220713828889795807412], [287496226244718057645479527259786527571014, 84786069214168511105657187029461690846650], [74157688622729732174811300059729595590668, 244347479687001491337365578074711728281651], [319415830137892143429822074121244263923880, 96030439351582956125714128743295441161476]], 'outer_group': '144.183', 'outer_hash': 183, 'outer_nilpotent': False, 'outer_order': 144, 'outer_permdeg': 7, 'outer_perms': [1, 120, 144, 3, 744, 1680], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_3\\times S_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [8, 10], [18, 6], [24, 2], [36, 9], [48, 4]], 'representations': {'PC': {'code': '3611570754937622791812401720245675751894474643911091661376521424352571836997694738161043827805237153866321796637973345923659083642575999', 'gens': [1, 2, 4, 5, 6, 7, 8, 9, 10], 'pres': [10, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 107640, 179001, 51, 489002, 35662, 616003, 96333, 21783, 138804, 38814, 624, 23134, 410405, 205935, 34585, 10295, 8865, 15136, 138247, 120977, 369368, 174978, 676809, 414419, 356429, 135039, 47749, 8759]}, 'Perm': {'d': 36, 'gens': [319415830137892143429822074121244263923880, 96033410119514675706661895146131406706161]}}, 'schur_multiplier': [3, 3, 3], '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': 'C_3^5:\\PSU(3,2)', 'transitive_degree': 36, '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: 153389473
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 421, 'group_order': 17496, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 153389484
    {'aut_label': '2A', 'centralizer': '81.a1', 'counter': 2, 'group_counter': 421, 'group_order': 17496, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 3785716297923801449284165417750754610, 'size': 81}
  • id: 153389495
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 3, 'group_counter': 421, 'group_order': 17496, 'label': '3A', 'order': 3, 'powers': [3, 1], 'representative': 20666822212130100088253110950034167978483, 'size': 2}
  • id: 153389506
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 4, 'group_counter': 421, 'group_order': 17496, 'label': '3B', 'order': 3, 'powers': [4, 1], 'representative': 20666567304132208352894533475407671405604, 'size': 2}
  • id: 153389513
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 421, 'group_order': 17496, 'label': '3C', 'order': 3, 'powers': [5, 1], 'representative': 20666822203593614219376205795957969040788, 'size': 2}
  • id: 153389514
    {'aut_label': '3D', 'centralizer': '4.a1', 'counter': 6, 'group_counter': 421, 'group_order': 17496, 'label': '3D', 'order': 3, 'powers': [6, 1], 'representative': 10628380765426167900161457350544321177603, 'size': 4}
  • id: 153389515
    {'aut_label': '3D', 'centralizer': '4.a1', 'counter': 7, 'group_counter': 421, 'group_order': 17496, 'label': '3E', 'order': 3, 'powers': [7, 1], 'representative': 526261674286189736370176755646672643, 'size': 4}
  • id: 153389516
    {'aut_label': '3D', 'centralizer': '4.a1', 'counter': 8, 'group_counter': 421, 'group_order': 17496, 'label': '3F', 'order': 3, 'powers': [8, 1], 'representative': 17683942790150574557177061504243, 'size': 4}
  • id: 153389517
    {'aut_label': '3G1', 'centralizer': '4.a1', 'counter': 9, 'group_counter': 421, 'group_order': 17496, 'label': '3G1', 'order': 3, 'powers': [10, 1], 'representative': 10628380783110079667891945245736960640244, 'size': 4}
  • id: 153389474
    {'aut_label': '3G1', 'centralizer': '4.a1', 'counter': 10, 'group_counter': 421, 'group_order': 17496, 'label': '3G-1', 'order': 3, 'powers': [9, 1], 'representative': 20666295941919359052059922281186744409747, 'size': 4}
  • id: 153389475
    {'aut_label': '3H', 'centralizer': '72.a1', 'counter': 11, 'group_counter': 421, 'group_order': 17496, 'label': '3H', 'order': 3, 'powers': [11, 1], 'representative': 2554923812208848884, 'size': 72}
  • id: 153389476
    {'aut_label': '3H', 'centralizer': '72.a1', 'counter': 12, 'group_counter': 421, 'group_order': 17496, 'label': '3I', 'order': 3, 'powers': [12, 1], 'representative': 3259537037682600982358200898580290164, 'size': 72}
  • id: 153389477
    {'aut_label': '3H', 'centralizer': '72.a1', 'counter': 13, 'group_counter': 421, 'group_order': 17496, 'label': '3J', 'order': 3, 'powers': [13, 1], 'representative': 3259537037682600984913082597447468307, 'size': 72}
  • id: 153389478
    {'aut_label': '3H', 'centralizer': '72.a1', 'counter': 14, 'group_counter': 421, 'group_order': 17496, 'label': '3K', 'order': 3, 'powers': [14, 1], 'representative': 3259537037682600987223628223764360880, 'size': 72}
  • id: 153389479
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 15, 'group_counter': 421, 'group_order': 17496, 'label': '3L1', 'order': 3, 'powers': [16, 1], 'representative': 418829649742661861079210387, 'size': 72}
  • id: 153389480
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 16, 'group_counter': 421, 'group_order': 17496, 'label': '3L-1', 'order': 3, 'powers': [15, 1], 'representative': 806634631152869842092717604, 'size': 72}
  • id: 153389481
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 17, 'group_counter': 421, 'group_order': 17496, 'label': '3M1', 'order': 3, 'powers': [18, 1], 'representative': 10631640302462625115550392403282403573360, 'size': 72}
  • id: 153389482
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 18, 'group_counter': 421, 'group_order': 17496, 'label': '3M-1', 'order': 3, 'powers': [17, 1], 'representative': 20669555469809584731768611078984462133363, 'size': 72}
  • id: 153389483
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 19, 'group_counter': 421, 'group_order': 17496, 'label': '3N1', 'order': 3, 'powers': [20, 1], 'representative': 10631640302462625115552947285249032645908, 'size': 72}
  • id: 153389485
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 20, 'group_counter': 421, 'group_order': 17496, 'label': '3N-1', 'order': 3, 'powers': [19, 1], 'representative': 20669555469809584731771165960938637164304, 'size': 72}
  • id: 153389486
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 21, 'group_counter': 421, 'group_order': 17496, 'label': '3O1', 'order': 3, 'powers': [22, 1], 'representative': 10631640302462625115555257830862895496883, 'size': 72}
  • id: 153389487
    {'aut_label': '3L1', 'centralizer': '72.a1', 'counter': 22, 'group_counter': 421, 'group_order': 17496, 'label': '3O-1', 'order': 3, 'powers': [21, 1], 'representative': 20669555469809584731773476506297192162484, 'size': 72}
  • id: 153389488
    {'aut_label': '3P', 'centralizer': '216.i1', 'counter': 23, 'group_counter': 421, 'group_order': 17496, 'label': '3P', 'order': 3, 'powers': [23, 1], 'representative': 255290879248901827705123684839112831861680, 'size': 216}
  • id: 153389489
    {'aut_label': '3P', 'centralizer': '216.i1', 'counter': 24, 'group_counter': 421, 'group_order': 17496, 'label': '3Q', 'order': 3, 'powers': [24, 1], 'representative': 138276935523415352574656910299320008042834, 'size': 216}
  • id: 153389490
    {'aut_label': '3P', 'centralizer': '216.i1', 'counter': 25, 'group_counter': 421, 'group_order': 17496, 'label': '3R', 'order': 3, 'powers': [25, 1], 'representative': 255290879248902634261069921295096191900227, 'size': 216}
  • id: 153389491
    {'aut_label': '3P', 'centralizer': '216.i1', 'counter': 26, 'group_counter': 421, 'group_order': 17496, 'label': '3S', 'order': 3, 'powers': [26, 1], 'representative': 255290624350050617355271803624828781960324, 'size': 216}
  • id: 153389492
    {'aut_label': '3P', 'centralizer': '216.i1', 'counter': 27, 'group_counter': 421, 'group_order': 17496, 'label': '3T', 'order': 3, 'powers': [27, 1], 'representative': 255294138776138704222445941778195307550324, 'size': 216}
  • id: 153389493
    {'aut_label': '3P', 'centralizer': '216.i1', 'counter': 28, 'group_counter': 421, 'group_order': 17496, 'label': '3U', 'order': 3, 'powers': [28, 1], 'representative': 275956648937684192992280109450342290293924, 'size': 216}
  • id: 153389494
    {'aut_label': '4A', 'centralizer': '1458.a1', 'counter': 29, 'group_counter': 421, 'group_order': 17496, 'label': '4A', 'order': 4, 'powers': [2, 29], 'representative': 233716654397025459991229251630740440722709, 'size': 1458}
  • id: 153389496
    {'aut_label': '4A', 'centralizer': '1458.a1', 'counter': 30, 'group_counter': 421, 'group_order': 17496, 'label': '4B', 'order': 4, 'powers': [2, 30], 'representative': 159857432700709105488731413620849206354373, 'size': 1458}
  • id: 153389497
    {'aut_label': '4A', 'centralizer': '1458.a1', 'counter': 31, 'group_counter': 421, 'group_order': 17496, 'label': '4C', 'order': 4, 'powers': [2, 31], 'representative': 191767275617379136553866389267396070373307, 'size': 1458}
  • id: 153389498
    {'aut_label': '6A', 'centralizer': '162.a1', 'counter': 32, 'group_counter': 421, 'group_order': 17496, 'label': '6A', 'order': 6, 'powers': [3, 2], 'representative': 10631640229197262430907216305830490524534, 'size': 162}
  • id: 153389499
    {'aut_label': '6A', 'centralizer': '162.a1', 'counter': 33, 'group_counter': 421, 'group_order': 17496, 'label': '6B', 'order': 6, 'powers': [4, 2], 'representative': 10635426036431908768065741768054795128274, 'size': 162}
  • id: 153389500
    {'aut_label': '6A', 'centralizer': '162.a1', 'counter': 34, 'group_counter': 421, 'group_order': 17496, 'label': '6C', 'order': 6, 'powers': [5, 2], 'representative': 138279668688878694372837870082711646929923, 'size': 162}
  • id: 153389501
    {'aut_label': '6D', 'centralizer': '324.a1', 'counter': 35, 'group_counter': 421, 'group_order': 17496, 'label': '6D', 'order': 6, 'powers': [6, 2], 'representative': 20666296161706979520094477476455131282084, 'size': 324}
  • id: 153389502
    {'aut_label': '6D', 'centralizer': '324.a1', 'counter': 36, 'group_counter': 421, 'group_order': 17496, 'label': '6E', 'order': 6, 'powers': [7, 2], 'representative': 127651814167442869872257342882587600999684, 'size': 324}
  • id: 153389503
    {'aut_label': '6D', 'centralizer': '324.a1', 'counter': 37, 'group_counter': 421, 'group_order': 17496, 'label': '6F', 'order': 6, 'powers': [8, 2], 'representative': 265921993179792113664486165410369139724948, 'size': 324}
  • id: 153389504
    {'aut_label': '6G1', 'centralizer': '324.a1', 'counter': 38, 'group_counter': 421, 'group_order': 17496, 'label': '6G1', 'order': 6, 'powers': [9, 2], 'representative': 20666296170243853196196172156687877685123, 'size': 324}
  • id: 153389505
    {'aut_label': '6G1', 'centralizer': '324.a1', 'counter': 39, 'group_counter': 421, 'group_order': 17496, 'label': '6G-1', 'order': 6, 'powers': [10, 2], 'representative': 10628380985212981809999465176645336718868, 'size': 324}
  • id: 153389507
    {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 40, 'group_counter': 421, 'group_order': 17496, 'label': '12A1', 'order': 12, 'powers': [32, 29], 'representative': 244347479777961251339582292037055240215925, 'size': 1458}
  • id: 153389508
    {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 41, 'group_counter': 421, 'group_order': 17496, 'label': '12A5', 'order': 12, 'powers': [32, 29], 'representative': 223680912482976112204142394137305053812546, 'size': 1458}
  • id: 153389509
    {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 42, 'group_counter': 421, 'group_order': 17496, 'label': '12B1', 'order': 12, 'powers': [33, 30], 'representative': 169892377118445667973660029249696879286643, 'size': 1458}
  • id: 153389510
    {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 43, 'group_counter': 421, 'group_order': 17496, 'label': '12B5', 'order': 12, 'powers': [33, 30], 'representative': 180521284136398246260925546183456653267264, 'size': 1458}
  • id: 153389511
    {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 44, 'group_counter': 421, 'group_order': 17496, 'label': '12C1', 'order': 12, 'powers': [34, 31], 'representative': 319410126323565641868065679222890723239800, 'size': 1458}
  • id: 153389512
    {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 45, 'group_counter': 421, 'group_order': 17496, 'label': '12C5', 'order': 12, 'powers': [34, 31], 'representative': 329447786574376610716451666970520309201948, 'size': 1458}
• 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: 14825590
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 14825601
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 14825612
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 14825620
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 14825621
    {'cdim': 2, 'counter': 5, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.2a', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825622
    {'cdim': 8, 'counter': 6, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8a', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825623
    {'cdim': 8, 'counter': 7, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8b', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, 8, -1, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825624
    {'cdim': 8, 'counter': 8, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8c', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, 8, -1, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825625
    {'cdim': 8, 'counter': 9, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8d', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825591
    {'cdim': 8, 'counter': 10, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8e', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, 2, -4, 5, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825592
    {'cdim': 8, 'counter': 11, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8f', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -4, 2, 5, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825593
    {'cdim': 8, 'counter': 12, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8g', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -4, 2, 2, -4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825594
    {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8h', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -4, 2, 2, 5, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825595
    {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8i', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 5, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825596
    {'cdim': 8, 'counter': 15, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.8j', 'multiplicity': 1, 'nt': [12, 174], 'qdim': 8, 'qvalues': [8, 0, 8, 8, 8, 8, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825599
    {'cdim': 18, 'counter': 18, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18a', 'multiplicity': 1, 'nt': [27, 420], 'qdim': 18, 'qvalues': [18, 2, -9, 18, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825600
    {'cdim': 18, 'counter': 19, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18b', 'multiplicity': 1, 'nt': [27, 420], 'qdim': 18, 'qvalues': [18, 2, 18, -9, 18, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -1, 2, -1, -1, 2, -1, -1, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
  • id: 14825602
    {'cdim': 18, 'counter': 20, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18c', 'multiplicity': 1, 'nt': [27, 420], 'qdim': 18, 'qvalues': [18, 2, 18, 18, -9, -9, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 14825603
    {'cdim': 18, 'counter': 21, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18d', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, -9, 18, 18, 18, -9, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825604
    {'cdim': 18, 'counter': 22, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18e', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, 18, -9, 18, -9, -9, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, -1, 2, -1, -1, 2, -1, -1, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
  • id: 14825605
    {'cdim': 18, 'counter': 23, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18f', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 2, 18, 18, -9, -9, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 14825597
    {'cdim': 12, 'counter': 16, 'faithful': True, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.12a', 'multiplicity': 2, 'nt': [36, 10766], 'qdim': 24, 'qvalues': [24, 8, -12, -12, -12, 6, 6, 6, -3, -3, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825598
    {'cdim': 12, 'counter': 17, 'faithful': True, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.12b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, -12, -12, -12, 6, 6, 6, -3, -3, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825606
    {'cdim': 18, 'counter': 24, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18g', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, -18, 36, 36, 36, -18, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825607
    {'cdim': 18, 'counter': 25, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18h', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, 36, -18, 36, -18, -18, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -4, 2, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825608
    {'cdim': 18, 'counter': 26, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.18i', 'multiplicity': 2, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, 36, 36, -18, -18, 36, -18, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825614
    {'cdim': 36, 'counter': 31, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.36a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 4, -18, -18, 36, -18, 9, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825615
    {'cdim': 36, 'counter': 32, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.36b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 4, -18, 36, -18, -18, -18, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825616
    {'cdim': 36, 'counter': 33, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.36c', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 36, 'qvalues': [36, 4, 36, -18, -18, 9, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825617
    {'cdim': 36, 'counter': 34, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.36d', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, -18, -18, 36, -18, 9, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825618
    {'cdim': 36, 'counter': 35, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.36e', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, -18, 36, -18, -18, -18, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825619
    {'cdim': 36, 'counter': 36, 'faithful': False, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.36f', 'multiplicity': 1, 'nt': [216, 0], 'qdim': 36, 'qvalues': [36, -4, 36, -18, -18, 9, -18, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 14825609
    {'cdim': 24, 'counter': 27, 'faithful': True, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.24a', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, 12, 12, 12, -6, -6, -6, -6, -6, 12, 3, 3, 3, 3, 3, 3, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825610
    {'cdim': 24, 'counter': 28, 'faithful': True, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.24b', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, 12, 12, 12, -6, -6, -6, -6, 12, -6, 3, 3, 3, 3, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825611
    {'cdim': 24, 'counter': 29, 'faithful': True, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.24c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, 12, 12, 12, -6, -6, -6, 12, -6, -6, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 14825613
    {'cdim': 24, 'counter': 30, 'faithful': True, 'group': '17496.qe', 'group_order': 17496, 'image': None, 'label': '17496.qe.24d', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, -24, -24, -24, 12, 12, 12, -6, -6, 12, -6, -6, -6, -6, -6, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 34475812
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 17496, 'label': '17496.qe.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34475823
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 8748, 'label': '17496.qe.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34475834
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 8748, 'label': '17496.qe.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34475845
    {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 8748, 'label': '17496.qe.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34475852
    {'center': '4.a1', 'center_index': 4, 'center_order': 4374, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.a1', 'kernel_order': 2187, 'label': '17496.qe.2a', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475853
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 6, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.qe.8a', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475854
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 7, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.qe.8b', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475855
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 8, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.qe.8c', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475856
    {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 9, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '72.41', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 243, 'label': '17496.qe.8d', 'nt': [9, 14], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475813
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 10, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.qe.8e', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475814
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 11, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.qe.8f', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[-4, 0]], [[2, 0]], [[5, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475815
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 12, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.qe.8g', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[5, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475816
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 13, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.qe.8h', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[5, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475817
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 14, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.qe.8i', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[2, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475818
    {'center': '648.a1', 'center_index': 648, 'center_order': 27, 'counter': 15, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '648.730', 'image_order': 648, 'indicator': 1, 'kernel': '648.a1', 'kernel_order': 27, 'label': '17496.qe.8j', 'nt': [12, 174], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 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]], [[5, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475819
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.12a1', 'nt': [36, 10766], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [3, 1]], [[-2, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475820
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.12a2', 'nt': [36, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0], [-3, 1]], [[1, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475821
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.12b1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0], [-9, 1]], [[3, 0], [9, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475822
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.12b2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0], [9, 1]], [[-6, 0], [-9, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475824
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 20, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18a', 'nt': [27, 420], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475825
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 21, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18b', 'nt': [27, 420], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475826
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 22, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18c', 'nt': [27, 420], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 34475827
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 23, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18d', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475828
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 24, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18e', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475829
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 25, 'cyclotomic_n': 1, 'dim': 18, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18f', 'nt': [54, 0], 'q_character': None, 'values': [[[18, 0]], [[2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 34475830
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 26, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18g1', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475831
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 27, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18g2', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[-9, 0]], [[18, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475832
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 28, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18h1', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 34475833
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 29, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18h2', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 34475835
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 30, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18i1', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]]]}
  • id: 34475836
    {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 31, 'cyclotomic_n': 12, 'dim': 18, 'faithful': False, 'field': [-3, 0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.3559', 'image_order': 1944, 'indicator': -1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.qe.18i2', 'nt': [216, 0], 'q_character': None, 'values': [[[18, 0]], [[-2, 0]], [[18, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
  • id: 34475837
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24a1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-12, 0], [-18, 1]], [[6, 0], [18, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475838
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24a2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0], [18, 1]], [[-12, 0], [-18, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475839
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24b1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-12, 0], [-18, 1]], [[6, 0], [18, 1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475840
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24b2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0], [18, 1]], [[-12, 0], [-18, 1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475841
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24c1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-12, 0], [-18, 1]], [[6, 0], [18, 1]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475842
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24c2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0], [18, 1]], [[-12, 0], [-18, 1]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475843
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24d1', 'nt': [72, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-12, 0], [-18, 1]], [[6, 0], [18, 1]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475844
    {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.qe', 'image_order': 17496, 'indicator': 0, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.qe.24d2', 'nt': [72, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0], [18, 1]], [[-12, 0], [-18, 1]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475846
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 40, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.qe.36a', 'nt': [54, 0], 'q_character': None, 'values': [[[36, 0]], [[4, 0]], [[-18, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[9, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475847
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 41, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.qe.36b', 'nt': [54, 0], 'q_character': None, 'values': [[[36, 0]], [[4, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475848
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 42, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': 1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.qe.36c', 'nt': [54, 0], 'q_character': None, 'values': [[[36, 0]], [[4, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475849
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 43, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': -1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.qe.36d', 'nt': [216, 0], 'q_character': None, 'values': [[[36, 0]], [[-4, 0]], [[-18, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[9, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475850
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 44, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': -1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.qe.36e', 'nt': [216, 0], 'q_character': None, 'values': [[[36, 0]], [[-4, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 34475851
    {'center': '5832.a1', 'center_index': 5832, 'center_order': 3, 'counter': 45, 'cyclotomic_n': 1, 'dim': 36, 'faithful': False, 'field': [0, 1], 'group': '17496.qe', 'group_counter': 421, 'group_order': 17496, 'image': None, 'image_isoclass': None, 'image_order': 5832, 'indicator': -1, 'kernel': '5832.a1', 'kernel_order': 3, 'label': '17496.qe.36f', 'nt': [216, 0], 'q_character': None, 'values': [[[36, 0]], [[-4, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 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: 157804554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '17496.qe.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '17496.qe', 'subgroup_hash': 785846807519522182, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^5:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 157804637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 8748, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.qe.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4208316362160278823, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^5.C_3^2.C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 4374, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.qe.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, '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', 'D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6153670493848560400, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^5.C_3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 2187, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '17496.qe.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L2', 'D2', 'C3', 'F', 'L2', 'D2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2187.6576', 'subgroup_hash': 3659524577990711916, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 157804670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1944.3929', 'subgroup_hash': 3929, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^5:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 157804681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1458.733', 'subgroup_hash': 733, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times \\He_3):S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804703
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '972.880', 'subgroup_hash': 880, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157804714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '972.773', 'subgroup_hash': 773, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.122', 'subgroup_hash': 122, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3:\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.425', 'subgroup_hash': 425, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '648.729', 'subgroup_hash': 729, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 157804588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 243, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.36.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.257', 'subgroup_hash': 257, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '486.183', 'subgroup_hash': 183, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 243, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.qe.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['C4', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
  • id: 157804643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '216.133', 'subgroup_hash': 133, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157804652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '216.161', 'subgroup_hash': 161, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 157804653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157804660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804662
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157804663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804666
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 157804667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157804669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 157804671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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: 157804673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157804677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157804682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804683
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157804684
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157804685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157804687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 157804691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, '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': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157804695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.243.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, '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': '72.41', 'subgroup_hash': 41, 'subgroup_order': 72, 'subgroup_tex': '\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
  • id: 157804696
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804701
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804702
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804706
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804711
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.324.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157804715
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 157804716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, '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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 157804717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.486.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, '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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 157804718
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': True, 'core_order': 27, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.qe.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.730', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 730, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S', 'D3', 'C5', 'Phi', 'S', 'D3', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804721
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.d2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 9, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804559
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804561
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804563
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804572
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.r3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.r3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804573
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.s2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.s2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804575
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804576
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.t2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 157804578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.648.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 157804580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.729.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '729.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 157804581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 157804584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.972.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 157804594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.1458.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, '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: 157804595
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1458.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 157804596
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1458.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1458.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1458, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 157804597
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 9, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '17496.qe.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1944.3559', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3559, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['C6', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 157804598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 3, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804600
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804605
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804609
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804611
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804613
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804614
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.1944.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1944, '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: 157804618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '17496.qe.2187.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2187.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2187, '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': 2}
  • id: 157804619
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.2916.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, '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: 157804620
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.2916.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, '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: 157804622
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.2916.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, '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: 157804623
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.2916.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2916.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, '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: 157804624
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.qe.2916.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2916.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2916, '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: 157804625
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.4374.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4374.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4374, '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: 157804626
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8748, 'characteristic': False, 'core_order': 3, 'counter': 164, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '17496.qe.5832.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5832.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5614895696097741054, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5832, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4.C_3^2.Q_8', 'simple': True, 'solvable': True, 'special_labels': ['C7', 'C7'], '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: 157804627
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.5832.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157804628
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4374, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.5832.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157804629
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.5832.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157804630
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.5832.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157804631
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.5832.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5832.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5832, '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: 157804633
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '17496.qe.8748.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8748.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8748, '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: 157804634
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '17496.qe', 'ambient_counter': 421, 'ambient_order': 17496, 'ambient_tex': 'C_3^5:\\PSU(3,2)', 'central': True, 'central_factor': False, 'centralizer_order': 17496, 'characteristic': True, 'core_order': 1, 'counter': 171, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '17496.qe.17496.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '17496.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '17496.qe', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 785846807519522182, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 17496, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^5:\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D4', 'C8', 'Z', 'PC', 'U0', 'D4', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 157804564
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['216.b1', '216.e1', '216.j1'], 'contains': ['1944.g1', '1944.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': [5987, -1, 6438, -1], 'generators': [265924963929405027525879606822916392805078, 255293883850456481889712000262093112435844, 9147456921273669403100862566548], 'label': '17496.qe.648.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.c1', 'old_label': '648.m1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157804554
    {'ambient': '17496.qe', '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': '17496.a1', 'complements': ['17496.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8634, 984, 1314, 2359], 'generators': [96033410119514675706661895146131406706161, 2554923812208848884, 3785816394267444306431359443190005120, 271353676394454377792702129150099764, 319415830137892143429822074121244263923880, 10628907044783140472034892274332109418480, 9147456921273669403100862566548, 127648554740305272909008102127952696481154, 237470756778666077357758918654224, 418829647187779894450137844], 'label': '17496.qe.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '17496.qe'}
  • id: 157804555
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '12.a1'], 'contains': ['72.b1', '72.c1', '72.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6122, -1, 5336, -1], 'generators': [265924963929405027525879606822916392805078, 271353676394454377792702129150099764, 265924963929404608696234730676633449973718, 9147456921273669403100862566548, 127651814259004856947509091436139462977280, 10628907044783140472034892274332109418480], 'label': '17496.qe.24.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157804556
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['216.d1', '216.g1', '324.j1'], 'contains': ['1944.d1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [9682, -1, 1920, -1], 'generators': [148317583938640153120611769655394687386884, 265918733752654128164275327743933019033204, 10628652128248793890219496307613835949508], 'label': '17496.qe.648.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '648.e2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804557
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.e1', '216.f1', '216.h1', '324.d1'], 'contains': ['1944.a1', '1944.c1', '1944.e1', '1944.f1', '1944.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3640, -1, 6973, -1], 'generators': [271371359111858934944111145713709600, 10628907036246685625578073782240332522387, 3785816394686195275878698685716396307], 'label': '17496.qe.648.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804558
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['216.e1', '216.g1', '216.i1', '324.e1'], 'contains': ['1944.a1', '1944.d1', '1944.h1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [8533, -1, 3836, -1], 'generators': [9147456921273669403100862566548, 6519074074170647194830904820331119283, 10628652136785279759096401461690034887203], 'label': '17496.qe.648.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '648.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804559
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.c1', '216.f1', '216.k1'], 'contains': ['1944.e1', '1944.g1', '1944.n1', '1944.n2', '1944.o1', '1944.r1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [1154, -1, 8941, -1], 'generators': [127646110343928631634559762767560113074373, 10628380774572399435841703605484685849744, 127648554740305691736407287364306740961014], 'label': '17496.qe.648.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.h1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804560
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['216.b1', '216.e1', '216.j1', '216.m1'], 'contains': ['1944.f1', '1944.g1', '1944.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': [5500, -1, 6845, -1], 'generators': [265924963929405027525879606822916392805078, 275960434700373701654703236294997810298948, 9147456921273669403100862566548], 'label': '17496.qe.648.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.c1', 'old_label': '648.i1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157804561
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.c1', '216.f1', '216.k1', '216.n1'], 'contains': ['1944.e1', '1944.f1', '1944.g1', '1944.n1', '1944.n2', '1944.o1', '1944.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [1431, -1, 8806, -1], 'generators': [20666295941919359052062477163140919440640, 10628380765426167900161457350544321177603, 418829647187779894450137844], 'label': '17496.qe.648.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.j1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804562
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['216.b1', '216.e1', '216.m1', '324.k1'], 'contains': ['1944.f1', '1944.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6223, -1, 6319, -1], 'generators': [148317583938640153120611769655394687386884, 3785816394686195273568153059399387764, 9147456921273669403100862566548], 'label': '17496.qe.648.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '648.k1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804563
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.c1', '216.f1', '216.n1', '324.l1'], 'contains': ['1944.e1', '1944.f1', '1944.o1', '1944.p1', '1944.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1860, -1, 8263, -1], 'generators': [10628652119101336968945826904512973382960, 3785816394686195273568153059399387764, 127648299832307412196071921860924484906690], 'label': '17496.qe.648.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '648.l1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157804565
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.h1', '216.j1', '216.k1', '216.m1', '216.n1', '324.f1'], 'contains': ['1944.e1', '1944.f1', '1944.g1', '1944.i1', '1944.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3214, -1, 7618, -1], 'generators': [271371359111858934944111145713709600, 3785816394686195275878698685716396307, 10628907044783140472034892274332109418480], 'label': '17496.qe.648.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.n1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804566
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.b1'], 'contains': ['72.a1', '72.b1', '72.c1', '72.d1', '72.f1', '72.f2', '72.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3681, -1, 7624, -1], 'generators': [271353676394454377792702129150099764, 265924963929404608696234730676633449973718, 9147456921273669403100862566548, 418829647187779894450137844, 127651814259004856947509091436139462977280, 10628907044783140472034892274332109418480], 'label': '17496.qe.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157804567
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.h1', '216.k2', '216.l1', '216.m1', '216.n1', '216.o1', '324.g1'], 'contains': ['1944.f1', '1944.i1', '1944.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [4024, -1, 7482, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 3785816394686195275878698685716396307], 'label': '17496.qe.648.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '648.o1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804568
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.h1', '216.j1', '216.k1', '216.k2', '216.p1'], 'contains': ['1944.g1', '1944.i1', '1944.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2881, -1, 8008, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 10635426118857698847769595203733066306064], 'label': '17496.qe.648.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '648.p1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.p1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157804569
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['216.i1', '216.j1', '216.l1', '216.m1', '216.p1', '324.h1'], 'contains': ['1944.h1', '1944.i1', '1944.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [6547, -1, 6718, -1], 'generators': [10628380783110079667891945245736960640244, 9147456921273669403100862566548, 6519074074170647194830904820331119283], 'label': '17496.qe.648.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.q1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.q1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804570
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c1', '216.k1'], 'contains': ['1944.j1', '1944.l1', '1944.n1', '1944.n2', '1944.p1', '1944.r1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [260, -1, 9348, -1], 'generators': [10628907044783140472034892274332109418480, 127645584082254376467243479253044196296130, 127648554740305691736407287364306740961014], 'label': '17496.qe.648.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.r1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804571
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.c1', '216.k1'], 'contains': ['1944.j1', '1944.l1', '1944.n1', '1944.o1', '1944.r1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [529, -1, 9077, -1], 'generators': [265924437667730741336145547191787063140930, 127651287997331796143366144407544314199044, 10628907044783140472034892274332109418480], 'label': '17496.qe.648.r2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.r2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804572
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.r3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c2', '216.k2'], 'contains': ['1944.k1', '1944.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [2166, -1, 8136, -1], 'generators': [127646110343928631634559762767560113074373, 10628380783110079667891945245736960640244, 271353675587898431557334130864237603], 'label': '17496.qe.648.r3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '648.r3', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157804573
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.a1', '216.l1'], 'contains': ['1944.k1', '1944.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [4174, -1, 7236, -1], 'generators': [6790436896408832266349848397756473200, 127645855435929964286992430718674882968774, 10628907044783140472034892274332109418480], 'label': '17496.qe.648.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1', 'old_label': '648.s1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.s1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157804574
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.s2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.a1', '216.l1', '324.m1'], 'contains': ['1944.k1', '1944.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4611, -1, 6590, -1], 'generators': [6519074074170647192520359194014226708, 10628907044783140472034892274332109418480, 265924437685414265296648934010915370404934], 'label': '17496.qe.648.s2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '648.s2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.s2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804575
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c1', '216.n1'], 'contains': ['1944.j1', '1944.k1', '1944.n1', '1944.o1', '1944.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1038, -1, 8670, -1], 'generators': [127651814259004856947509091436139462977280, 265924963929405027525881917368542709813573, 10628907044783140472034892274332109418480], 'label': '17496.qe.648.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.t1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804576
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.t2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.c1', '216.n1', '324.n1'], 'contains': ['1944.j1', '1944.k1', '1944.n2', '1944.o1', '1944.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1646, -1, 8534, -1], 'generators': [127645584090790831313700296699008932833878, 10628907044783140472034892274332109418480, 127648554740305691736407287364306740961014], 'label': '17496.qe.648.t2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '648.t2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.t2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804577
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['9.a1'], 'contains': ['54.c1', '54.d1', '81.b1', '243.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [8474, -1, 990, -1], 'generators': [319415830137892143429822074121244263923880, 271371359111858934944111145713709600, 265924963929405027525881917368542709813573, 106071325296007448058142057023113496391826, 148317583938640153120609214731582478538384, 10628907036246685625578073782240332522387, 10628907264571179767458901851061427691443], 'label': '17496.qe.27.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
  • id: 157804578
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c2', '216.o1', '324.o1'], 'contains': ['1944.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2678, -1, 7881, -1], 'generators': [10628380783110079667891945245736960640244, 418829647187779894450137844, 127645584082254376467243479253044196296130], 'label': '17496.qe.648.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '648.u1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804579
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['216.a1', '216.p1'], 'contains': ['1944.l1', '1944.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1728, 'diagramx': [3371, -1, 7355, -1], 'generators': [271362822657012478125619053936813507, 255296056911451642628710709070866237413174, 10631911665285282128025963098524131653908], 'label': '17496.qe.648.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.b1', 'old_label': '648.v1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 157804580
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '729.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['81.b1', '243.a1'], 'contains': ['1458.a1', '1458.b1', '2187.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 2187, 'diagramx': [9140, -1, 141, -1], 'generators': [319415830137892143429822074121244263923880, 361357892657892630139979903267335105388405, 275962353017599447518624187151693252586240, 10628652128248793890219496307613835949508], 'label': '17496.qe.729.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '729.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157804581
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.a1', '324.b1', '324.b2', '324.c1', '486.a1'], 'contains': ['1944.b1', '2916.a1', '2916.b1', '2916.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [7138, -1, 3655, -1], 'generators': [271362822657012478125619053936813507, 10628907036246685625578073782240332522387, 237470756778666077357758918654224], 'label': '17496.qe.972.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '972.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804582
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['324.a1', '324.d1', '324.e1', '486.b1', '486.c1'], 'contains': ['1944.a1', '2916.a1', '2916.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8548, -1, 3081, -1], 'generators': [9147456921273669403100862566548, 237470756778666077357758918654224, 10628652136785279759096401461690034887203], 'label': '17496.qe.972.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '972.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157804583
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.f1', '324.g1', '324.h1'], 'contains': ['1944.i1', '2916.b1', '2916.c1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [6377, -1, 5062, -1], 'generators': [271353676394454377792702129150099764, 10628907027100423067477740865315545808644, 237470756778666077357758918654224], 'label': '17496.qe.972.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '972.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804584
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['324.b1', '324.b2', '324.d1', '324.i1'], 'contains': ['1944.c1', '2916.a1', '2916.d1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [5620, -1, 4016, -1], 'generators': [148314850682224631882390527300521467674194, 10628652128248793890219496307613835949508, 237470756778666077357758918654224], 'label': '17496.qe.972.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804585
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['324.c1', '324.e1', '324.j1'], 'contains': ['1944.d1', '2916.a1', '2916.e1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [9497, -1, 2840, -1], 'generators': [275957175199358060354610116283680160750723, 10628652128248793890219496307613835949508, 237470756778666077357758918654224], 'label': '17496.qe.972.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804586
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['324.b1', '324.d1', '324.f1', '324.l1'], 'contains': ['1944.e1', '2916.b1', '2916.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [5287, -1, 4837, -1], 'generators': [10628380774572399435841703605484685849744, 237470756778666077357758918654224, 148314595774226740147031706535438845700437], 'label': '17496.qe.972.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804587
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['324.b2', '324.d1', '324.f1', '324.g1', '324.k1', '324.l1'], 'contains': ['1944.f1', '2916.b1', '2916.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [5865, -1, 4613, -1], 'generators': [138276680597733549071565291093673737450693, 271353676394454377792702129150099764, 237470756778666077357758918654224], 'label': '17496.qe.972.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804588
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.a1', '12.b1'], 'contains': ['72.b1', '108.a1', '108.b1', '108.c1', '108.j1'], 'core': '648.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5426, -1, 5037, -1], 'generators': [271353676394454377792702129150099764, 265924963929404608696234730676633449973718, 9147456921273669403100862566548, 6519074074170647192520359194014226708, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '36.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804589
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['324.c1', '324.e1', '324.h1', '324.k1'], 'contains': ['1944.h1', '2916.b1', '2916.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [7853, -1, 3430, -1], 'generators': [255290624340904354797166605280591265343508, 271353676394454377792702129150099764, 237470756778666077357758918654224], 'label': '17496.qe.972.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.h1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804590
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['324.b1', '324.b2', '324.f1', '324.n1'], 'contains': ['1944.j1', '2916.c1', '2916.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [4689, -1, 5287, -1], 'generators': [271362822657012478125619053936813507, 138276409261741097407345493300101895470050, 237470756778666077357758918654224], 'label': '17496.qe.972.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.i1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804591
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.b1', '324.g1', '324.m1', '324.n1', '324.o1'], 'contains': ['1944.k1', '2916.c1', '2916.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4880, -1, 5783, -1], 'generators': [10628907027100423067477740865315545808644, 127648554740305272909010655963779831027654, 237470756778666077357758918654224], 'label': '17496.qe.972.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '972.j1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804592
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['324.c1', '324.h1', '324.m1'], 'contains': ['1944.m1', '2916.c1', '2916.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': [6623, -1, 4390, -1], 'generators': [271362822657012478125619053936813507, 237470756778666077357758918654224, 255290624350050617355266937109530977881203], 'label': '17496.qe.972.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '972.k1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804593
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['324.i1', '324.l1', '324.n1', '486.d1'], 'contains': ['1944.q1', '2916.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3951, -1, 4203, -1], 'generators': [148317583938640153120609214731582478538384, 265924437667730741336145547191787063140930, 237470756778666077357758918654224], 'label': '17496.qe.972.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '972.l1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804594
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1458.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['162.b1', '162.d1', '486.a1', '486.b1', '729.a1'], 'contains': ['2916.a1', '4374.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 2187, 'diagramx': [9108, -1, 901, -1], 'generators': [180523457197384986705591992361920681238358, 10628907036246685625578073782240332522387, 127645855326042849420365016793872864127413], 'label': '17496.qe.1458.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '1458.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804595
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1458.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['162.c1', '486.b1', '486.c1', '729.a1'], 'contains': ['2916.a1', '4374.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': [8859, -1, 732, -1], 'generators': [6518991648349468631664257368648487493, 116699179790613098154209401921154659591921, 10628652136785279759096401461690034887203], 'label': '17496.qe.1458.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '1458.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157804596
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1458.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['162.e1', '486.a1', '486.c1'], 'contains': ['2916.b1', '4374.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': [8103, -1, 1070, -1], 'generators': [319415830137892143429822074121244263923880, 275962879279273702685933050315084230496563, 10628380774572399435841703605484685849744], 'label': '17496.qe.1458.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '1458.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804597
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['648.a1', '648.f1', '648.g1', '972.b1'], 'contains': ['5832.a1', '5832.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7691, 2800, 4771, 6340], 'generators': [9147456921273669403100862566548, 10628652136785279759096401461690034887203], 'label': '17496.qe.1944.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': ['648.a1'], 'normal_contains': ['5832.a1'], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': '17496.qe', 'quotient_action_image': '4.2', 'quotient_action_kernel': '486.249', 'quotient_action_kernel_order': 486, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157804598
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['648.a1', '648.b1', '648.b2', '648.c1', '972.a1'], 'contains': ['5832.a1', '5832.b1', '5832.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6008, -1, 6455, -1], 'generators': [271362822657012478125619053936813507, 10628907036246685625578073782240332522387], 'label': '17496.qe.1944.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '1944.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804599
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['12.a1', '12.b1'], 'contains': ['72.c1', '108.a1', '108.b1', '108.d1', '108.g1', '108.k1'], 'core': '648.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6341, -1, 4382, -1], 'generators': [265918733752653709413310502542082497564324, 3785816394686195273568153059399387764, 271353676394454377792702129150099764, 9147456921273669403100862566548, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '36.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804600
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.b1', '648.b2', '648.d1', '648.d2', '648.f1', '972.d1'], 'contains': ['5832.a1', '5832.d1', '5832.e1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3053, -1, 7482, -1], 'generators': [127648554740305272909010655963779831027654, 10628652136785279759096401461690034887203], 'label': '17496.qe.1944.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '1944.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804601
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['648.c1', '648.e1', '648.e2', '648.g1', '972.e1'], 'contains': ['5832.a1', '5832.f1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [9374, -1, 3836, -1], 'generators': [3785816395074002502979816608198533760, 10628652136785279759096401461690034887203], 'label': '17496.qe.1944.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '1944.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804602
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.b1', '648.f1', '648.h1', '648.j1', '648.l1', '648.n1', '972.f1'], 'contains': ['5832.b1', '5832.d1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2400, -1, 7753, -1], 'generators': [2554923812208848884, 10628380774572399435841703605484685849744], 'label': '17496.qe.1944.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '1944.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804603
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.b2', '648.f1', '648.i1', '648.j1', '648.k1', '648.l1', '648.n1', '648.o1', '972.g1'], 'contains': ['5832.b1', '5832.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3913, -1, 7108, -1], 'generators': [271371359111858934944111145713709600, 2554923812208848884], 'label': '17496.qe.1944.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '1944.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804604
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.b2', '648.f1', '648.h1', '648.i1', '648.j1', '648.m1', '648.n1', '648.p1'], 'contains': ['5832.b1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3510, -1, 7295, -1], 'generators': [271371359111858934944111145713709600, 10635426118857698847769595203733066306064], 'label': '17496.qe.1944.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '1944.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157804605
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['648.c1', '648.g1', '648.i1', '648.k1', '648.m1', '648.q1', '972.h1'], 'contains': ['5832.b1', '5832.f1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [7315, -1, 6319, -1], 'generators': [9147456921273669403100862566548, 3785816394267444308742951209001414004], 'label': '17496.qe.1944.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '1944.h1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804606
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.n1', '648.o1', '648.p1', '648.q1', '972.c1'], 'contains': ['5832.b1', '5832.c1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4907, -1, 6726, -1], 'generators': [271353676394454377792702129150099764, 10628907027100423067477740865315545808644], 'label': '17496.qe.1944.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '1944.i1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804607
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.b1', '648.b2', '648.n1', '648.r1', '648.r2', '648.t1', '648.t2', '972.i1'], 'contains': ['5832.c1', '5832.d1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2059, -1, 8025, -1], 'generators': [2554923812208848884, 10628907027100423067477740865315545808644], 'label': '17496.qe.1944.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '1944.j1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804608
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.b1', '648.o1', '648.r3', '648.s1', '648.s2', '648.t1', '648.t2', '648.u1', '972.j1'], 'contains': ['5832.c1', '5832.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2892, -1, 7618, -1], 'generators': [271362822657012478125619053936813507, 2554923812208848884], 'label': '17496.qe.1944.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '1944.k1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804609
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.b1', '648.p1', '648.r1', '648.r2', '648.r3', '648.v1'], 'contains': ['5832.c1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1765, -1, 8160, -1], 'generators': [271362822657012478125619053936813507, 10628907044783140472030025759034305223108], 'label': '17496.qe.1944.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '1944.l1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.l1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157804610
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1'], 'contains': ['72.d1', '108.a1', '108.e1', '108.m1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3236, -1, 7067, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 418829647187779894450137844, 237470756778666077357758918654224, 10628907044783140472034892274332109418480, 127645855435929545536027848807025302543094], 'label': '17496.qe.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '36.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804611
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['648.c1', '648.q1', '648.s1', '648.s2', '648.v1', '972.k1'], 'contains': ['5832.c1', '5832.f1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [5755, -1, 6590, -1], 'generators': [10628380783110079667891945245736960640244, 3785816394267444308742951209001414004], 'label': '17496.qe.1944.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '1944.m1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804612
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.d1', '648.d2', '648.h1', '648.j1', '648.r1', '648.r2', '648.t1'], 'contains': ['5832.d1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [636, -1, 8806, -1], 'generators': [3785816394686195273568153059399387764, 148314595774226740147031706535438845700437], 'label': '17496.qe.1944.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '1944.n1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804613
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.d1', '648.h1', '648.j1', '648.r1', '648.t2'], 'contains': ['5832.d1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1442, -1, 8941, -1], 'generators': [265924709039089853195080491302932776850530, 127651814259004856947509091436139462977280], 'label': '17496.qe.1944.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '1944.n2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.n2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804614
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['648.d1', '648.h1', '648.j1', '648.l1', '648.r2', '648.t1', '648.t2'], 'contains': ['5832.d1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [1120, -1, 8534, -1], 'generators': [148311880023563927731227836574125683016277, 127648554740305691736407287364306740961014], 'label': '17496.qe.1944.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '1944.o1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804615
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.d1', '648.j1', '648.l1', '648.r1', '648.t1'], 'contains': ['5832.d1', '5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [475, -1, 8670, -1], 'generators': [127645855435929545536027848807025302543094, 127648554740305691736407287364306740961014], 'label': '17496.qe.1944.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '1944.p1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804616
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['648.d2', '648.l1', '648.t2', '972.l1'], 'contains': ['5832.d1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2516, -1, 7889, -1], 'generators': [271353676394454380104335472779264243, 418829647187779894450137844], 'label': '17496.qe.1944.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1944.q1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.q1', 'subgroup_fusion': None, 'weyl_group': '8.4'}
  • id: 157804617
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '1944.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['648.d1', '648.h1', '648.r1', '648.r2'], 'contains': ['5832.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [45, -1, 9077, -1], 'generators': [148314324420550345692661334184702396257158, 10631911665285282128025963098524131653908], 'label': '17496.qe.1944.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '1944.r1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804618
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2187.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['243.b1', '729.a1'], 'contains': ['4374.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2187, 'diagramx': [8128, -1, 249, -1], 'generators': [319415830137892143429822074121244263923880, 361357892657892630139979903267335105388405, 265924964103390288221010011649889716026403], 'label': '17496.qe.2187.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2187.a1', 'old_label': '2187.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2187.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157804619
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2916.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['972.a1', '972.b1', '972.d1', '972.e1', '1458.a1', '1458.b1'], 'contains': ['5832.a1', '8748.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [9009, -1, 3442, -1], 'generators': [10628907036246685625578073782240332522387, 237470756778666077357758918654224], 'label': '17496.qe.2916.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '2916.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804620
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2916.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['972.a1', '972.b1', '972.c1', '972.f1', '972.g1', '972.h1', '1458.c1'], 'contains': ['5832.b1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [6415, -1, 4598, -1], 'generators': [10628380765426167900161457350544321177603, 237470756778666077357758918654224], 'label': '17496.qe.2916.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1', 'old_label': '2916.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804621
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '36.c2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '18.a1'], 'contains': ['72.a1', '108.a1', '108.e2', '108.h1', '108.l1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4863, -1, 4709, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 127651814259004856947509091436139462977280, 265924963929405027525881917368542709813573, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.36.c2', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.c2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c2', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804622
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2916.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.a1', '972.c1', '972.i1', '972.j1', '972.k1'], 'contains': ['5832.c1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5808, -1, 5062, -1], 'generators': [237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.2916.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '2916.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804623
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2916.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['972.d1', '972.f1', '972.g1', '972.i1', '972.j1', '972.l1'], 'contains': ['5832.d1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5103, -1, 4898, -1], 'generators': [138276680597733549071565291093673737450693, 237470756778666077357758918654224], 'label': '17496.qe.2916.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '2916.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804624
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2916.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['972.e1', '972.h1', '972.k1'], 'contains': ['5832.f1', '8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [8181, -1, 4390, -1], 'generators': [255290352987227960342796232929587054005824, 237470756778666077357758918654224], 'label': '17496.qe.2916.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '2916.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804625
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '4374.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['486.d1', '1458.a1', '1458.b1', '1458.c1', '2187.a1'], 'contains': ['8748.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2187, 'diagramx': [7942, -1, 985, -1], 'generators': [6518991648349468631664257368648487493, 116699179790613098154209401921154659591921], 'label': '17496.qe.4374.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.a1', 'old_label': '4374.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4374.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804626
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '5832.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['1944.a1', '1944.b1', '1944.c1', '1944.d1', '2916.a1'], 'contains': ['17496.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8229, 2800, 5479, 6340], 'generators': [10628652128248793890219496307613835949508], 'label': '17496.qe.5832.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '5832.a1', 'normal_contained_in': ['1944.a1'], 'normal_contains': ['17496.a1'], 'normalizer': '1.a1', 'old_label': '5832.a1', 'projective_image': '17496.qe', 'quotient_action_image': '2.1', 'quotient_action_kernel': None, 'quotient_action_kernel_order': 2916, 'quotient_fusion': None, 'short_label': '5832.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804627
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '5832.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1944.a1', '1944.b1', '1944.e1', '1944.f1', '1944.g1', '1944.h1', '1944.i1', '2916.b1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5440, -1, 6496, -1], 'generators': [10628380765426167900161457350544321177603], 'label': '17496.qe.5832.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '5832.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804628
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '5832.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1944.b1', '1944.i1', '1944.j1', '1944.k1', '1944.l1', '1944.m1', '2916.c1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3693, -1, 6658, -1], 'generators': [10628907044783140472034892274332109418480], 'label': '17496.qe.5832.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '5832.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804629
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '5832.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1944.c1', '1944.e1', '1944.f1', '1944.j1', '1944.k1', '1944.n1', '1944.n2', '1944.o1', '1944.p1', '1944.q1', '2916.d1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2489, -1, 7821, -1], 'generators': [3785816394686195275878698685716396307], 'label': '17496.qe.5832.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '5832.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804630
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '5832.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1944.c1', '1944.e1', '1944.g1', '1944.j1', '1944.l1', '1944.n1', '1944.n2', '1944.o1', '1944.p1', '1944.r1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1953, -1, 8160, -1], 'generators': [10628907044783140472030025759034305223108], 'label': '17496.qe.5832.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '5832.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804631
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '5832.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1944.d1', '1944.h1', '1944.m1', '2916.e1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [8098, -1, 6319, -1], 'generators': [6519074074170647194830904820331119283], 'label': '17496.qe.5832.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '5832.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 157804632
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['12.a1', '18.b1'], 'contains': ['72.e1', '108.b1', '108.f1', '108.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [9044, -1, 2777, -1], 'generators': [6519074073751819795645668466286639428, 271353676394454377792702129150099764, 9147456921273669403100862566548, 237470756778666077357758918654224, 265921993279890585930623027496428643316084, 10628907044783140472034892274332109418480], 'label': '17496.qe.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804633
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '8748.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2916.a1', '2916.b1', '2916.c1', '2916.d1', '2916.e1', '4374.a1'], 'contains': ['17496.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5916, -1, 4598, -1], 'generators': [237470756778666077357758918654224], 'label': '17496.qe.8748.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '8748.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8748.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804634
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '17496.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5832.a1', '5832.b1', '5832.c1', '5832.d1', '5832.e1', '5832.f1', '8748.a1'], 'contains': [], 'core': '17496.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5440, 2800, 6496, 6340], 'generators': [], 'label': '17496.qe.17496.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '17496.a1', 'normal_contained_in': ['5832.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804635
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1'], 'contains': ['72.g1', '108.j1', '108.k1', '108.l1', '108.m1'], 'core': '17496.a1', 'coset_action_label': '36T10766', 'count': 48, 'diagramx': [5122, -1, 5758, -1], 'generators': [10631911665284863298378775318629797638000, 10628380783110079667891945245736960640244, 138276680615416266476122442502958062954934, 9147456921273669403100862566548, 237470756778666077357758918654224, 418829647187779894450137844], 'label': '17496.qe.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804636
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['18.a1'], 'contains': ['108.e2', '162.b1', '162.e1', '486.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [7157, -1, 2274, -1], 'generators': [319415830137892143429822074121244263923880, 3785816394686195273568153059399387764, 271353676394454377792702129150099764, 228933883104814939056625827307680, 127648554740305272909010655963779831027654, 10628907044783140472034892274332109418480], 'label': '17496.qe.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157804637
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '18.a1', '18.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8563, 984, 1404, 2359], 'generators': [2554923812208848884, 3785816394267444306431359443190005120, 271353676394454377792702129150099764, 319415830137892143429822074121244263923880, 10628907044783140472034892274332109418480, 9147456921273669403100862566548, 127648554740305272909008102127952696481154, 237470756778666077357758918654224, 418829647187779894450137844], 'label': '17496.qe.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 157804638
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['18.b1'], 'contains': ['108.f1', '162.d1', '486.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [9636, -1, 1255, -1], 'generators': [6519074073751819795645668466286639428, 271362822657012478125619053936813507, 319415830137892143429822074121244263923880, 10628907246887267999730968837822963134084, 10628907027100423067477740865315545808644, 255293883850456900719356876408376171514804], 'label': '17496.qe.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '54.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157804639
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['18.a1', '27.a1'], 'contains': ['108.h1', '162.b1', '162.c1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [8332, -1, 1639, -1], 'generators': [96033410119514675706661895146131406706161, 138273964838533056345031129635928721825974, 10628652136785279759096401461690034887203, 9147456921273669403100862566548, 138276680615416685227094444765732705395894, 237471175529638079620801199736384], 'label': '17496.qe.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157804640
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['18.a1', '27.a1'], 'contains': ['108.h1', '162.c1', '162.e1', '486.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7884, -1, 1956, -1], 'generators': [319415830137892143429822074121244263923880, 10628907264570792038914406601383691876483, 3785816394686195273568153059399387764, 271353676394454377792702129150099764, 10628907036246685625578073782240332522387, 127648554740305272909010655963779831027654], 'label': '17496.qe.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
  • id: 157804641
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['18.b1'], 'contains': ['108.i1', '162.d1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [9305, -1, 805, -1], 'generators': [319415830137892143429822074121244263923880, 271371359111858934944111145713709600, 275960434700373701654703236294997810298948, 10628907036246685625578073782240332522387, 237471175529638079620801199736384, 255290624350050617355271803624828781960324], 'label': '17496.qe.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '54.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157804642
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': ['243.b1'], 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '36.c2'], 'contains': ['216.c1', '216.f1', '216.h1', '216.k1', '216.n1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2166, 9016, 9540, 8973], 'generators': [2554923812208848884, 271353676394454377792702129150099764, 9147456921273669403100862566548, 418829647187779894450137844, 10628907044783140472034892274332109418480], 'label': '17496.qe.72.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '17496.qe', 'quotient_action_image': '72.41', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804643
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.b1', '36.a1'], 'contains': ['216.a1', '216.h1', '216.i1', '216.l1', '216.p1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [3913, -1, 6736, -1], 'generators': [127651814259005275777156278128048838939124, 271353676394454377792702129150099764, 9147456921273669403100862566548, 3785816394267444308742951209001414004, 10628907044783140472034892274332109418480], 'label': '17496.qe.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157804644
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['24.a1', '24.b1', '36.b1'], 'contains': ['216.b1', '216.e1', '216.h1', '216.i1', '216.j1', '216.m1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6122, -1, 6382, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 418829647187779894450137844, 3785816394267444308742951209001414004, 10628907044783140472034892274332109418480], 'label': '17496.qe.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157804645
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.c1'], 'contains': ['216.c2', '216.h1', '216.k2', '216.o1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2569, -1, 7896, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 418829647187779894450137844, 10628907044783140472034892274332109418480, 127645855435929545536027848807025302543094], 'label': '17496.qe.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157804646
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['24.a1', '36.d1'], 'contains': ['216.d1', '216.g1', '216.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8995, -1, 2898, -1], 'generators': [265921993279890167103226396095901740766324, 271353676394454377792702129150099764, 9147456921273669403100862566548, 6519074074170647192520359194014226708, 10628907044783140472034892274332109418480], 'label': '17496.qe.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
  • id: 157804647
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.b1'], 'contains': ['216.j1', '216.k1', '216.k2', '216.m1', '216.p1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [3517, -1, 8354, -1], 'generators': [3785816394267444306431359443190005120, 271353676394454377792702129150099764, 148314324420550764522306210330985331946838, 10628907027100423067477740865315545808644, 127648554740305272909010655963779831027654], 'label': '17496.qe.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '72.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157804648
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.a1', '12.b1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6123, 984, 4913, 2359], 'generators': [3785816394267444306431359443190005120, 127648554740305272909008102127952696481154, 2554923812208848884, 271353676394454377792702129150099764, 9147456921273669403100862566548, 418829647187779894450137844, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157804649
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.f2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1'], 'contains': ['216.j1', '216.k2', '216.l1', '216.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3062, -1, 8167, -1], 'generators': [3785816394267444306431359443190005120, 271353676394454377792702129150099764, 10628907027100423067477740865315545808644, 148314324420550345692661334184702396257158, 127648554740305691736407287364306740961014], 'label': '17496.qe.72.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '72.f2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f2', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157804650
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '36.e1'], 'contains': ['216.l1', '216.m1', '216.n1', '216.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3681, -1, 7624, -1], 'generators': [3785816394267444306431359443190005120, 10628380783110079667891945245736960640244, 9147456921273669403100862566548, 418829647187779894450137844, 127648554740305272909010655963779831027654], 'label': '17496.qe.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '72.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804651
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['162.a1', '243.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8924, -1, 163, -1], 'generators': [319415830137892143429822074121244263923880, 265924964094242831299736343335041689530308, 271353676394454377792702129150099764, 9147456921273669403100862566548, 351319977472862565336705449498470327109765, 10628907044783140472034892274332109418480], 'label': '17496.qe.81.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 157804652
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['27.a1'], 'contains': ['162.b1', '162.c1', '243.b1', '729.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [7776, -1, 403, -1], 'generators': [319415830137892143429822074121244263923880, 351320248835684384743833813804984304245266, 20666295941919359052062477163140919440640, 10628907036246685625578073782240332522387, 265924709195391620952132462530173360588947, 526261674673996963471294678128810480], 'label': '17496.qe.81.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '81.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157804653
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.c2'], 'contains': ['216.h1', '324.a1', '324.b1', '324.b2', '324.d1', '324.f1', '324.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5639, -1, 4701, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 127648554740305272909010655963779831027654, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '108.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804654
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.a1', '36.b1', '36.d1'], 'contains': ['216.i1', '324.a1', '324.c1', '324.e1', '324.h1'], 'core': '648.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [8230, -1, 3204, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 265918733752654128164277639335698830325827, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '108.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804655
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['36.a1'], 'contains': ['216.a1', '324.b1', '324.c1', '324.m1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [4918, -1, 4986, -1], 'generators': [271353676394454377792702129150099764, 127645855435929964286992430718674882968774, 6519091757694609946219179491399701680, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804656
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['36.b1'], 'contains': ['216.b1', '324.b2', '324.c1', '324.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6999, -1, 3798, -1], 'generators': [265918733752653709413310502542082497564324, 271353676394454377792702129150099764, 237470756778666077357758918654224, 10628907044783140472034892274332109418480, 127648554740305691736407287364306740961014], 'label': '17496.qe.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804657
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.c1'], 'contains': ['216.c2', '324.b1', '324.o1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2861, -1, 7376, -1], 'generators': [17684330597377674587114469465744, 127645855444467225768078089400870321039237, 271353676394454377792702129150099764, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '108.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804658
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.c2', '54.a1'], 'contains': ['216.c1', '324.b1', '324.b2', '324.i1', '324.l1', '324.n1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4125, -1, 4416, -1], 'generators': [271362822657012478125619053936813507, 127645855426783314000347602593918063605730, 237470756778666077357758918654224, 10628907044783140472034892274332109418480, 127648554740305691736407287364306740961014], 'label': '17496.qe.108.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.e2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804659
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': ['2187.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1'], 'contains': ['24.a1', '24.b1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6060, 984, 5336, 2359], 'generators': [3785816394267444306431359443190005120, 127648554740305272909008102127952696481154, 2554923812208848884, 271353676394454377792702129150099764, 9147456921273669403100862566548, 418829647187779894450137844, 10628907044783140472034892274332109418480], 'label': '17496.qe.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '17496.qe', 'quotient_action_image': '8.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
  • id: 157804660
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['36.d1', '54.b1'], 'contains': ['216.d1', '324.c1', '324.j1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [9794, -1, 2567, -1], 'generators': [6519074073751819795645668466286639428, 271362822657012478125619053936813507, 275960434700374120405675238557772336734228, 10628907027100423067477740865315545808644, 237470756778666077357758918654224], 'label': '17496.qe.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804661
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['36.b1'], 'contains': ['216.e1', '324.d1', '324.e1', '324.k1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [7716, -1, 3488, -1], 'generators': [271353676394454377792702129150099764, 10628907036246685625578073782240332522387, 237470756778666077357758918654224, 275957175199357641524962928503785833992468, 127648554740305691736407287364306740961014], 'label': '17496.qe.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804662
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.c2', '54.c1', '54.d1'], 'contains': ['216.f1', '324.d1', '324.i1', '324.l1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4654, -1, 4107, -1], 'generators': [271371359111858934944111145713709600, 10628907036246685625578073782240332522387, 148314324420550345692661334184702396257158, 237470756778666077357758918654224, 10631911665285282128025963098524131653908], 'label': '17496.qe.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.h1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804663
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['36.d1', '54.e1'], 'contains': ['216.g1', '324.e1', '324.j1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [9385, -1, 2257, -1], 'generators': [271371359111858934944111145713709600, 255293883850456481889712000262093112435844, 10628907036246685625578073782240332522387, 237470756778666077357758918654224, 255290624350050617355271803624828781960324], 'label': '17496.qe.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.i1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804664
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.a1', '36.e1'], 'contains': ['216.l1', '324.g1', '324.h1', '324.m1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [5396, -1, 5914, -1], 'generators': [20669555469809165904369424754645227355524, 10628380783110079667891945245736960640244, 9147456921273669403100862566548, 148317583938640571871576351567044274954244, 237470756778666077357758918654224], 'label': '17496.qe.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.j1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804665
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['36.b1', '36.e1'], 'contains': ['216.m1', '324.f1', '324.g1', '324.h1', '324.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [6199, -1, 5295, -1], 'generators': [3785816394686195273568153059399387764, 271353676394454377792702129150099764, 9147456921273669403100862566548, 237470756778666077357758918654224, 127645855435929545536027848807025302543094], 'label': '17496.qe.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '108.k1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804666
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.c2', '36.e1'], 'contains': ['216.n1', '324.f1', '324.g1', '324.l1', '324.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4390, -1, 5604, -1], 'generators': [271353676394454377792702129150099764, 10628907027100423067477740865315545808644, 148312406285236988535370783602988593688918, 237470756778666077357758918654224, 127648554740305691736407287364306740961014], 'label': '17496.qe.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '108.l1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804667
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1', '36.e1'], 'contains': ['216.o1', '324.g1', '324.o1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3232, -1, 7067, -1], 'generators': [10628380783110079667891945245736960640244, 9147456921273669403100862566548, 418829647187779894450137844, 237470756778666077357758918654224, 138273964838533056345031129635928721825974], 'label': '17496.qe.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '108.m1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804668
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.a1', '18.b1', '81.a1'], 'contains': ['324.a1', '486.a1', '486.b1', '486.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8732, -1, 620, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 6519000795806389905333660214203201234, 96033410119514675706661895146131406706161, 10628907044783140472034892274332109418480], 'label': '17496.qe.162.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157804669
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['54.a1', '54.c1', '81.b1'], 'contains': ['324.i1', '486.d1', '1458.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [7274, -1, 1620, -1], 'generators': [127646110343928631634559762767560113074373, 148314850682225019689615073494644071751554, 96033410119514675706661895146131406706161, 237471175529638079620801199736384, 10628652128248793890219496307613835949508], 'label': '17496.qe.162.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '162.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804670
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['18.a1', '27.a1', '81.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8763, -1, 1222, -1], 'generators': [219788039374111481918426296398867, 319415830137892143429822074121244263923880, 106071070378862937006852151106801158168325, 271353676394454377792702129150099764, 9147456921273669403100862566548, 127651814259004856947509091436139462977280, 265924963929405027525881917368542709813573, 10628907044783140472034892274332109418480], 'label': '17496.qe.9.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '1944.3929'}
  • id: 157804671
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['54.c1', '54.d1', '81.b1'], 'contains': ['324.i1', '486.d1', '1458.b1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [7524, -1, 1329, -1], 'generators': [10628907036246685625578073782240332522387, 148314324420550764522306210330985331946838, 237471175529638079620801199736384, 96033155229199113595616562866982805454786, 127645855435929545536027848807025302543094], 'label': '17496.qe.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
  • id: 157804672
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['54.b1', '54.e1'], 'contains': ['324.j1', '1458.a1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': [9662, -1, 894, -1], 'generators': [255290624350050198527867751873176933400964, 180523457197384986705591992361920681238358, 127651287997330989587419907951560954160883, 10628907036246685625578073782240332522387, 237471175529638079620801199736384], 'label': '17496.qe.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.d1', 'old_label': '162.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804673
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['54.a1', '54.d1'], 'contains': ['324.l1', '486.d1', '1458.c1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6757, -1, 1974, -1], 'generators': [106070799025186930332727995515055337313525, 10628380985213400639646651868554596558723, 10628380765426167900161457350544321177603, 127648554740305272909010655963779831027654, 20670081731483839899082582960156749621120], 'label': '17496.qe.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '162.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '108.37'}
  • id: 157804674
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['72.b1', '108.c1'], 'contains': ['648.b1', '648.c1', '648.s1', '648.s2', '648.v1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [4327, -1, 6754, -1], 'generators': [127651814259005275777156278128048838939124, 271353676394454377792702129150099764, 3785816394267444308742951209001414004, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '216.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804675
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '108.d1'], 'contains': ['648.b2', '648.c1', '648.i1', '648.k1', '648.m1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6291, -1, 6435, -1], 'generators': [271362822657012478125619053936813507, 265924963929405027525879606822916392805078, 10628907036246685625578073782240332522387, 127648554740305272909010655963779831027654], 'label': '17496.qe.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '216.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804676
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.a1', '108.e2'], 'contains': ['648.b1', '648.b2', '648.d1', '648.d2', '648.h1', '648.j1', '648.l1', '648.r1', '648.r2', '648.t1', '648.t2'], 'core': '5832.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1431, -1, 9811, -1], 'generators': [271362822657012478125619053936813507, 127651814259004856947509091436139462977280, 265924963929405027525881917368542709813573, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 157804677
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.c2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.d1', '108.e1'], 'contains': ['648.b1', '648.r3', '648.u1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2283, -1, 8993, -1], 'generators': [271362822657012478125619053936813507, 10628907036246685625578073782240332522387, 418829647187779894450137844, 127645855435929545536027848807025302543094], 'label': '17496.qe.216.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '216.c2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804678
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.e1', '108.f1'], 'contains': ['648.c1', '648.e1', '648.e2'], 'core': '5832.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [9955, -1, 2138, -1], 'generators': [271353676394454377792702129150099764, 265924963929404608696234730676633449973718, 127645855435929964286992430718674882968774, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804679
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '108.g1'], 'contains': ['648.f1', '648.g1', '648.i1', '648.k1', '648.m1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [6564, -1, 6115, -1], 'generators': [265921993279890167103226396095901740766324, 271353676394454377792702129150099764, 10628907036246685625578073782240332522387, 418829647187779894450137844], 'label': '17496.qe.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '216.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804680
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.a1', '108.h1'], 'contains': ['648.d1', '648.d2', '648.f1', '648.h1', '648.j1', '648.l1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1807, -1, 9676, -1], 'generators': [9147456921273669403100862566548, 127651814259004856947509091436139462977280, 265924963929405027525881917368542709813573, 10628652136785279759096401461690034887203], 'label': '17496.qe.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '8.4'}
  • id: 157804681
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1'], 'contains': ['24.a1', '36.a1', '36.b1', '36.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6212, -1, 4769, -1], 'generators': [3785816394267444306431359443190005120, 2554923812208848884, 271353676394454377792702129150099764, 9147456921273669403100862566548, 237470756778666077357758918654224, 10628907044783140472034892274332109418480, 127648554740305691736407287364306740961014], 'label': '17496.qe.12.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '12.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804682
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.e1', '108.i1'], 'contains': ['648.e1', '648.e2', '648.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [9445, -1, 1819, -1], 'generators': [6519074073751819795645668466286639428, 127651814259005275777156278128048838939124, 271353676394454377792702129150099764, 10628907036246685625578073782240332522387], 'label': '17496.qe.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '216.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804683
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.d1', '108.a1'], 'contains': ['648.a1', '648.b1', '648.b2', '648.f1', '648.n1', '648.o1', '648.p1'], 'core': '648.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2881, -1, 7621, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 127648554740305272909010655963779831027654, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.h1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804684
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.b1', '72.c1', '72.e1', '108.b1'], 'contains': ['648.a1', '648.c1', '648.g1', '648.q1'], 'core': '648.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7976, -1, 5169, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 3785816394267444308742951209001414004, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.i1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804685
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.c1', '72.f1', '72.f2'], 'contains': ['648.i1', '648.m1', '648.n1', '648.p1', '648.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [5366, -1, 8035, -1], 'generators': [20673086369668279861952465120079016594804, 271353676394454377792702129150099764, 10628907027100423067477740865315545808644, 6519074074170647192520359194014226708], 'label': '17496.qe.216.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '216.j1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157804686
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.f1'], 'contains': ['648.h1', '648.j1', '648.n1', '648.p1', '648.r1', '648.r2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1292, -1, 9947, -1], 'generators': [271353676394454377792702129150099764, 418829647187779894450137844, 10628907027100423067477740865315545808644, 20666567295594528120846603426921207897604], 'label': '17496.qe.216.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '216.k1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 157804687
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.f1', '72.f2'], 'contains': ['648.o1', '648.p1', '648.r3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [2556, -1, 9312, -1], 'generators': [10628380783110079667891945245736960640244, 9147456921273669403100862566548, 20666567295594946871811428628771613254964, 148312406285236988535370783602988593688918], 'label': '17496.qe.216.k2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '216.k2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k2', 'subgroup_fusion': None, 'weyl_group': '81.15'}
  • id: 157804688
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.f2', '72.g1', '108.j1'], 'contains': ['648.o1', '648.q1', '648.s1', '648.s2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3892, -1, 7073, -1], 'generators': [271371359111858934944111145713709600, 265921993262207449698669244686617415262083, 127651814259005275777156278128048838939124, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.l1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804689
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.c1', '72.f1', '72.g1', '108.k1'], 'contains': ['648.i1', '648.k1', '648.n1', '648.o1', '648.q1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5748, -1, 7393, -1], 'generators': [6519074073751819795645668466286639428, 271353676394454377792702129150099764, 10628907027100423067477740865315545808644, 6519074074170647192520359194014226708], 'label': '17496.qe.216.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.m1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804690
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.f2', '72.g1', '108.l1'], 'contains': ['648.j1', '648.l1', '648.n1', '648.o1', '648.t1', '648.t2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2088, -1, 9540, -1], 'generators': [3785816394686195273568153059399387764, 271353676394454377792702129150099764, 10628907027100423067477740865315545808644, 127648554740305272909010655963779831027654], 'label': '17496.qe.216.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.n1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804691
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.g1', '108.m1'], 'contains': ['648.o1', '648.u1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3130, -1, 8673, -1], 'generators': [10628380783110079667891945245736960640244, 9147456921273669403100862566548, 418829647187779894450137844, 138273964838533056345031129635928721825974], 'label': '17496.qe.216.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.o1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
  • id: 157804692
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['24.b1', '36.a1', '36.b1', '36.c1', '36.c2', '36.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5058, -1, 5058, -1], 'generators': [3785816394267444306431359443190005120, 271353676394454377792702129150099764, 9147456921273669403100862566548, 127648554740305272909010655963779831027654, 237470756778666077357758918654224, 10628907044783140472034892274332109418480, 127648554740305691736407287364306740961014], 'label': '17496.qe.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '12.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 157804693
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.b1', '72.f1'], 'contains': ['648.p1', '648.q1', '648.v1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [3403, -1, 8354, -1], 'generators': [6519074073751819795645668466286639428, 271371359111858934944111145713709600, 127645855435929964286992430718674882968774, 10628907044783140472034892274332109418480], 'label': '17496.qe.216.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '216.p1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
  • id: 157804694
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.a1', '81.a1'], 'contains': ['486.b1', '486.c1', '729.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 729, 'diagramx': [9107, -1, 79, -1], 'generators': [275962624371274616587408313415473541043204, 319415830137892143429822074121244263923880, 271353676394454377792702129150099764, 10628907036246685625578073782240332522387, 351319977472862565336705449498470327109765], 'label': '17496.qe.243.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '243.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157804695
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['81.b1'], 'contains': ['486.d1', '2187.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [7363, -1, 318, -1], 'generators': [319415830137892143429822074121244263923880, 116699706052286965565997752368379717621285, 228933883104814939056625827307680, 127648028478632212104874885995841041569013, 3259554720400005544375037495635823523], 'label': '17496.qe.243.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '243.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804696
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '162.a1'], 'contains': ['648.a1', '972.a1', '972.b1', '972.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7832, -1, 2946, -1], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.324.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157804697
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['108.a1', '108.c1', '108.e1', '108.e2'], 'contains': ['648.b1', '972.a1', '972.d1', '972.f1', '972.i1', '972.j1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [4290, -1, 4714, -1], 'generators': [3785807858200326398974590749011858564, 271362822657012478125619053936813507, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804698
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.b2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['108.a1', '108.d1', '108.e2'], 'contains': ['648.b2', '972.a1', '972.d1', '972.g1', '972.i1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [5775, -1, 3923, -1], 'generators': [271371359111858934944111145713709600, 10628907027100423067477740865315545808644, 237470756778666077357758918654224, 20669555469809584731768611078984462133363], 'label': '17496.qe.324.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.b2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804699
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['108.b1', '108.c1', '108.d1', '108.f1'], 'contains': ['648.c1', '972.a1', '972.e1', '972.h1', '972.k1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 3888, 'diagramx': [8161, -1, 2686, -1], 'generators': [271362822657012478125619053936813507, 20669555469809165904369424754645227355524, 10628907027100423067477740865315545808644, 237470756778666077357758918654224], 'label': '17496.qe.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804700
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['108.a1', '108.g1', '108.h1'], 'contains': ['648.f1', '972.b1', '972.d1', '972.f1', '972.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [7016, -1, 3665, -1], 'generators': [10631911665285282128028517980490760610483, 271371359111858934944111145713709600, 10628907036246685625578073782240332522387, 237470756778666077357758918654224], 'label': '17496.qe.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804701
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['108.b1', '108.g1', '108.i1'], 'contains': ['648.g1', '972.b1', '972.e1', '972.h1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [8703, -1, 2428, -1], 'generators': [271371359111858934944111145713709600, 10628907036246685625578073782240332522387, 3785816394267444308742951209001414004, 237470756778666077357758918654224], 'label': '17496.qe.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804702
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['108.a1', '108.k1', '108.l1'], 'contains': ['648.n1', '972.c1', '972.f1', '972.g1', '972.i1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [5554, -1, 4972, -1], 'generators': [271371359111858934944111145713709600, 3785798710743405125305229493729068400, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.f1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804703
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.c2', '54.a1', '54.c1', '54.d1', '162.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8332, -1, 1639, -1], 'generators': [2554923812208848884, 271353676394454377792702129150099764, 9147456921273669403100862566548, 6519000794999833963963719528647368194, 418829647187779894450137844, 96033410119514675706661895146131406706161, 10628907044783140472034892274332109418480], 'label': '17496.qe.18.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '648.729'}
  • id: 157804704
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.j1', '108.k1', '108.l1', '108.m1'], 'contains': ['648.o1', '972.c1', '972.g1', '972.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5173, -1, 5826, -1], 'generators': [2554923812208848884, 271353676394454377792702129150099764, 9147456921273669403100862566548, 237470756778666077357758918654224], 'label': '17496.qe.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1', 'old_label': '324.g1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804705
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['108.b1', '108.j1', '108.k1'], 'contains': ['648.q1', '972.c1', '972.h1', '972.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': [7395, -1, 4456, -1], 'generators': [271371359111858934944111145713709600, 265918733761800359699957884502654120821920, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1', 'old_label': '324.h1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804706
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['108.e2', '108.h1', '162.b1', '162.c1'], 'contains': ['648.d2', '972.d1', '972.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3686, -1, 3214, -1], 'generators': [10628907036246685625578073782240332522387, 148314324420550345692661334184702396257158, 20670081731483839899082582960156749621120, 237470756778666077357758918654224], 'label': '17496.qe.324.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.i1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804707
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['108.f1', '108.i1', '162.d1'], 'contains': ['648.e2', '972.e1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [9764, -1, 1566, -1], 'generators': [20670081731483452094105794931388419986560, 275962352852761612720099119231852525010290, 10628652128248793890219496307613835949508, 237470756778666077357758918654224], 'label': '17496.qe.324.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.j1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804708
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['108.d1', '108.g1', '108.k1'], 'contains': ['648.k1', '972.g1', '972.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [7206, -1, 3444, -1], 'generators': [265921993279890167103226396095901740766324, 3785807858200326396662998995654491664, 271353676394454377792702129150099764, 237470756778666077357758918654224], 'label': '17496.qe.324.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '324.k1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804709
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['108.e2', '108.h1', '108.l1', '162.e1'], 'contains': ['648.l1', '972.f1', '972.g1', '972.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4679, -1, 4190, -1], 'generators': [20666295941919359052062477163140919440640, 10628380774572399435841703605484685849744, 237470756778666077357758918654224, 20666295941919746780606972412830993049600], 'label': '17496.qe.324.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '324.l1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 157804710
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.c1', '108.j1'], 'contains': ['648.s2', '972.j1', '972.k1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [4983, -1, 5604, -1], 'generators': [3259546183526408115554282361577845268, 265919260023474645889684523782658511733684, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.324.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '324.m1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804711
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.e2', '108.l1'], 'contains': ['648.t2', '972.i1', '972.j1', '972.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3237, -1, 5374, -1], 'generators': [3530899859114227864505748247572370707, 127648554749452729830284325366612931699797, 237470756778666077357758918654224, 10628907044783140472034892274332109418480], 'label': '17496.qe.324.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c2', 'old_label': '324.n1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804712
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '324.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1', '108.m1'], 'contains': ['648.u1', '972.j1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2665, -1, 7781, -1], 'generators': [17684330597377674587114469465744, 10628380783110079667891945245736960640244, 127645584090790831313700296699008932833878, 237470756778666077357758918654224], 'label': '17496.qe.324.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '324.o1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804713
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['54.a1', '54.b1', '162.a1'], 'contains': ['972.a1', '1458.a1', '1458.c1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': [8527, -1, 1070, -1], 'generators': [319415830137892143429822074121244263923880, 271353676394454377792702129150099764, 265924964103390288221010011649889716026403, 10628907044783140472034892274332109418480], 'label': '17496.qe.486.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '486.a1', 'old_label': '486.a1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804714
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['2.a1'], 'contains': ['36.d1', '54.b1', '54.e1', '162.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [9044, -1, 1295, -1], 'generators': [265918733752653709413310502542082497564324, 127651814259005275777156278128048838939124, 271353676394454377792702129150099764, 9147456921273669403100862566548, 180523457197384986705591992361920681238358, 237471175529638079620801199736384, 10628907044783140472034892274332109418480], 'label': '17496.qe.18.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '18.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '324.163'}
  • id: 157804715
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['54.c1', '54.e1', '162.a1', '243.a1'], 'contains': ['972.b1', '1458.a1', '1458.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 1458, 'diagramx': [9245, -1, 418, -1], 'generators': [271371359111858934944111145713709600, 180523457197384986705591992361920681238358, 10628907036246685625578073782240332522387, 127645855326042849420365016793872864127413], 'label': '17496.qe.486.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1', 'old_label': '486.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 157804716
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['54.d1', '162.a1', '243.a1'], 'contains': ['972.b1', '1458.b1', '1458.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8994, -1, 712, -1], 'generators': [271371359111858934944111145713709600, 20673086295780557821526197732521012040290, 10628907036246685625578073782240332522387, 96033155229199113595616562866982805454786], 'label': '17496.qe.486.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 157804717
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '486.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['162.b1', '162.c1', '162.e1', '243.b1'], 'contains': ['972.l1', '4374.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [6766, -1, 1309, -1], 'generators': [6790345323937367060666667431996139330, 116699179790613098154209401921154659591921, 9146650365327433993256996928003, 526270820517725411750962537701549364], 'label': '17496.qe.486.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1', 'old_label': '486.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.d1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
  • id: 157804718
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.h1', '216.i1', '324.a1'], 'contains': ['1944.a1', '1944.b1', '1944.i1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7419, 2800, 5603, 6340], 'generators': [271353676394454377792702129150099764, 9147456921273669403100862566548, 10628907044783140472034892274332109418480], 'label': '17496.qe.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['72.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '17496.qe', 'quotient_action_image': '4.2', 'quotient_action_kernel': '162.54', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 157804719
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.a1', '216.c1', '216.c2', '216.h1', '324.b1'], 'contains': ['1944.b1', '1944.c1', '1944.e1', '1944.j1', '1944.k1', '1944.l1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2570, -1, 7753, -1], 'generators': [271362822657012478125619053936813507, 10628907036246685625578073782240332522387, 3785816394686195275878698685716396307], 'label': '17496.qe.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.b1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804720
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.b2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.b1', '216.c1', '216.h1', '324.b2'], 'contains': ['1944.b1', '1944.c1', '1944.f1', '1944.g1', '1944.j1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3524, -1, 7108, -1], 'generators': [9147456921273669403100862566548, 3785816394686195275878698685716396307, 10628907044783140472034892274332109418480], 'label': '17496.qe.648.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.b2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 157804721
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['216.a1', '216.b1', '216.d1', '216.i1', '324.c1'], 'contains': ['1944.b1', '1944.d1', '1944.h1', '1944.m1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [7589, -1, 5467, -1], 'generators': [271362822657012478125619053936813507, 10628907036246685625578073782240332522387, 265918733752654128164277639335698830325827], 'label': '17496.qe.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '648.c1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 157804722
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.c1', '216.f1'], 'contains': ['1944.c1', '1944.n1', '1944.n2', '1944.o1', '1944.p1', '1944.r1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [747, -1, 9213, -1], 'generators': [10628907036246685625578073782240332522387, 127651814259004856947509091436139462977280, 265924963929405027525881917368542709813573], 'label': '17496.qe.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '648.d1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 157804723
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.d2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['216.c1', '216.f1', '324.i1'], 'contains': ['1944.c1', '1944.n1', '1944.q1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2030, -1, 8399, -1], 'generators': [3785816394686195273568153059399387764, 127648299841453643731752168115877303620438, 10628652136785279759096401461690034887203], 'label': '17496.qe.648.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.d2', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d2', 'subgroup_fusion': None, 'weyl_group': '8.4'}
  • id: 157804724
    {'ambient': '17496.qe', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['216.d1', '216.g1'], 'contains': ['1944.d1'], 'core': '5832.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [9784, -1, 2138, -1], 'generators': [127645855435929964286992430718674882968774, 10628907036246685625578073782240332522387, 3259554721206640165795922346090741363], 'label': '17496.qe.648.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1', 'old_label': '648.e1', 'projective_image': '17496.qe', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '9.2'}