Abstract group data - 5516.b

Formats: - HTML - YAML - JSON - 2025-10-06T21:36:00.749265

• 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': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '28.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 38612, 'aut_gen_orders': [196, 197], 'aut_gens': [[1, 28], [3921, 896], [5321, 28]], 'aut_group': '38612.a', 'aut_hash': 3526511167592259168, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 38612, 'aut_permdeg': 394, 'aut_perms': [17606807853436041742251222907423391029521104053525232793571392754422346124118519681687484966106991063205565346901128005818043569366287657016119718300336824862715202223355396098733202338095261760845047855603230736646934838911149693119758108967374735919988384824366129742828215916036416008758875451117662836208864989426550034254391651337854395748457349147882290171453101745580249195836188835364065452076646388663709490639373160243314246904019199425038408492873213388965762092137956427357772063146685447591801606201795441798679170405722116796767947790028065869578616386587319520031886393645409997276136169774914202151902262257927737515194721997603857145461522271159709602220715473371132277999624756025186605440808823691427364157662013542925927351120595898247210349042828158576158108093201506818619117974028539604141696734989834268158054559905697402425116, 8922354001202601160363426660920225440256300688234399865413088840456414146700516923215059539897090843623636072037056728496796208222653913863943136615352492898663373093045221340566762590977521272839801889445500180004402315783030946508131652042561975102728885658286742091309389295736926118547607621741810614986879824524618696305225713109131781147540344659211792755040141141004577835822900717172062278004258097376919041337929376550378574691272723892514343574025084645644295217754531583947845406101104744252211145870087777838152013156712851933015695858867909832715473899785651854060955994922891747337405513811224601073867069327383495858768017131708596098480978711020451216447663414286444179987501993016179083986111621689002521581660812360757193692898080722269204950381364191544898156839499445208325752706370944053626320901404313531324095662138195005287056080], 'aut_phi_ratio': 16.416666666666668, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 197, 1, 1], [4, 197, 1, 2], [7, 197, 1, 6], [14, 197, 1, 6], [28, 197, 1, 12], [197, 28, 7, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{197}', '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': 38612, 'autcentquo_group': '38612.a', 'autcentquo_hash': 3526511167592259168, 'autcentquo_nilpotent': False, 'autcentquo_order': 38612, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{197}', 'cc_stats': [[1, 1, 1], [2, 197, 1], [4, 197, 2], [7, 197, 6], [14, 197, 6], [28, 197, 12], [197, 28, 7]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5516.b', 'commutator_count': 1, 'commutator_label': '197.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '197.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 197, 1, 1], [4, 197, 2, 1], [7, 197, 6, 1], [14, 197, 6, 1], [28, 197, 12, 1], [197, 28, 7, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 5516, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 7, 197], 'factors_of_order': [2, 7, 197], 'faithful_reps': [[28, 1, 7]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '5516.b', 'hash': 3, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 5516, 'inner_gen_orders': [28, 197], 'inner_gens': [[1, 3612], [1933, 28]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 5516, 'inner_split': False, 'inner_tex': 'C_{197}:C_{28}', 'inner_used': [1, 2], 'irrC_degree': 28, 'irrQ_degree': 196, 'irrQ_dim': 196, 'irrR_degree': 28, 'irrep_stats': [[1, 28], [28, 7]], 'label': '5516.b', 'linC_count': 7, 'linC_degree': 28, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 196, 'linQ_degree_count': 1, 'linQ_dim': 196, 'linQ_dim_count': 1, 'linR_count': 7, 'linR_degree': 28, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C197:C28', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 29, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 35, 'number_divisions': 7, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 12, 'number_subgroups': 992, 'old_label': None, 'order': 5516, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 197], [4, 394], [7, 1182], [14, 1182], [28, 2364], [197, 196]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 7, 'outer_gen_orders': [7], 'outer_gen_pows': [15], 'outer_gens': [[1, 2100]], 'outer_group': '7.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 7, 'outer_permdeg': 7, 'outer_perms': [873], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_7', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 197, 'pgroup': 0, 'primary_abelian_invariants': [4, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [6, 2], [12, 1], [196, 1]], 'representations': {'PC': {'code': '123824184051505935950752245655', 'gens': [1, 4], 'pres': [4, -2, -2, -7, -197, 8, 21, 57795, 20839, 19947]}, 'GLFp': {'d': 2, 'p': 197, 'gens': [1230905137, 7645571]}, 'Perm': {'d': 197, 'gens': [329954749323943683485414640837628795855009464308884797389926009175910253225649213518660315031949992785885892202931628519514293177717339680025473886652325415486195584477580675201722646012891130311262658073916565438400217548472199275759571395797662222012750598888228673866474206663587574582919125445066141436950555088710810940306064537650665216145769396583004635646709, 83798066828474758962615765428081992116221523017082802213627923002170787251655253719718761976496741589626409269183514085479709407030172024388460358849454082917936147893994000632898072331855406488258126493721310200181827856730135947236884043665001217177059437553402881687383510308733297246851762285007802721854589462563845456263162977445428137096779147093725928052520, 267106199558061214658488776598343768354426702668607914730690128099844625533217979768811516409198477468496245890031712814755750989237943436398602614050036465674556360984469182235876735223801293346281494169651441446360080826558496212255915381467483506360546147998294252541134642233524082895597071843697904255254523429616852571479713529143006206879624907079813248209333, 99570393372994116545053621392809991743215031488961728865427440048454375266082666326285866899454578360975475219524434206830245409279616608778483002673441726977088385078413145934338802813359727508617103740958928960810158648814977950333626518167340628844823362087763843223581053406560943668904006630292962961731996627658342400000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [28], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{197}:C_{28}', 'transitive_degree': 197, '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: 110602377
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2, 'group_order': 5516, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
  • id: 110602388
    {'aut_label': '2A', 'centralizer': '197.a1.a1', 'counter': 2, 'group_counter': 2, 'group_order': 5516, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 798, 'size': 197}
  • id: 110602399
    {'aut_label': '4A1', 'centralizer': '197.a1.a1', 'counter': 3, 'group_counter': 2, 'group_order': 5516, 'label': '4A1', 'order': 4, 'powers': [2, 4, 4, 3], 'representative': 371, 'size': 197}
  • id: 110602406
    {'aut_label': '4A-1', 'centralizer': '197.a1.a1', 'counter': 4, 'group_counter': 2, 'group_order': 5516, 'label': '4A-1', 'order': 4, 'powers': [2, 3, 3, 4], 'representative': 441, 'size': 197}
  • id: 110602407
    {'aut_label': '7A1', 'centralizer': '197.a1.a1', 'counter': 5, 'group_counter': 2, 'group_order': 5516, 'label': '7A1', 'order': 7, 'powers': [7, 9, 1, 5], 'representative': 3768, 'size': 197}
  • id: 110602408
    {'aut_label': '7A-1', 'centralizer': '197.a1.a1', 'counter': 6, 'group_counter': 2, 'group_order': 5516, 'label': '7A-1', 'order': 7, 'powers': [8, 10, 1, 6], 'representative': 2840, 'size': 197}
  • id: 110602409
    {'aut_label': '7A2', 'centralizer': '197.a1.a1', 'counter': 7, 'group_counter': 2, 'group_order': 5516, 'label': '7A2', 'order': 7, 'powers': [10, 6, 1, 7], 'representative': 2328, 'size': 197}
  • id: 110602410
    {'aut_label': '7A-2', 'centralizer': '197.a1.a1', 'counter': 8, 'group_counter': 2, 'group_order': 5516, 'label': '7A-2', 'order': 7, 'powers': [9, 5, 1, 8], 'representative': 5372, 'size': 197}
  • id: 110602411
    {'aut_label': '7A3', 'centralizer': '197.a1.a1', 'counter': 9, 'group_counter': 2, 'group_order': 5516, 'label': '7A3', 'order': 7, 'powers': [6, 7, 1, 9], 'representative': 2764, 'size': 197}
  • id: 110602378
    {'aut_label': '7A-3', 'centralizer': '197.a1.a1', 'counter': 10, 'group_counter': 2, 'group_order': 5516, 'label': '7A-3', 'order': 7, 'powers': [5, 8, 1, 10], 'representative': 2304, 'size': 197}
  • id: 110602379
    {'aut_label': '14A1', 'centralizer': '197.a1.a1', 'counter': 11, 'group_counter': 2, 'group_order': 5516, 'label': '14A1', 'order': 14, 'powers': [5, 13, 2, 11], 'representative': 4026, 'size': 197}
  • id: 110602380
    {'aut_label': '14A-1', 'centralizer': '197.a1.a1', 'counter': 12, 'group_counter': 2, 'group_order': 5516, 'label': '14A-1', 'order': 14, 'powers': [6, 14, 2, 12], 'representative': 3562, 'size': 197}
  • id: 110602381
    {'aut_label': '14A3', 'centralizer': '197.a1.a1', 'counter': 13, 'group_counter': 2, 'group_order': 5516, 'label': '14A3', 'order': 14, 'powers': [9, 16, 2, 13], 'representative': 962, 'size': 197}
  • id: 110602382
    {'aut_label': '14A-3', 'centralizer': '197.a1.a1', 'counter': 14, 'group_counter': 2, 'group_order': 5516, 'label': '14A-3', 'order': 14, 'powers': [10, 15, 2, 14], 'representative': 3994, 'size': 197}
  • id: 110602383
    {'aut_label': '14A5', 'centralizer': '197.a1.a1', 'counter': 15, 'group_counter': 2, 'group_order': 5516, 'label': '14A5', 'order': 14, 'powers': [8, 11, 2, 15], 'representative': 3498, 'size': 197}
  • id: 110602384
    {'aut_label': '14A-5', 'centralizer': '197.a1.a1', 'counter': 16, 'group_counter': 2, 'group_order': 5516, 'label': '14A-5', 'order': 14, 'powers': [7, 12, 2, 16], 'representative': 2550, 'size': 197}
  • id: 110602385
    {'aut_label': '28A1', 'centralizer': '197.a1.a1', 'counter': 17, 'group_counter': 2, 'group_order': 5516, 'label': '28A1', 'order': 28, 'powers': [11, 19, 3, 17], 'representative': 5401, 'size': 197}
  • id: 110602386
    {'aut_label': '28A-1', 'centralizer': '197.a1.a1', 'counter': 18, 'group_counter': 2, 'group_order': 5516, 'label': '28A-1', 'order': 28, 'powers': [12, 20, 4, 18], 'representative': 2719, 'size': 197}
  • id: 110602387
    {'aut_label': '28A3', 'centralizer': '197.a1.a1', 'counter': 19, 'group_counter': 2, 'group_order': 5516, 'label': '28A3', 'order': 28, 'powers': [13, 23, 4, 19], 'representative': 4919, 'size': 197}
  • id: 110602389
    {'aut_label': '28A-3', 'centralizer': '197.a1.a1', 'counter': 20, 'group_counter': 2, 'group_order': 5516, 'label': '28A-3', 'order': 28, 'powers': [14, 24, 3, 20], 'representative': 3313, 'size': 197}
  • id: 110602390
    {'aut_label': '28A5', 'centralizer': '197.a1.a1', 'counter': 21, 'group_counter': 2, 'group_order': 5516, 'label': '28A5', 'order': 28, 'powers': [15, 28, 3, 21], 'representative': 237, 'size': 197}
  • id: 110602391
    {'aut_label': '28A-5', 'centralizer': '197.a1.a1', 'counter': 22, 'group_counter': 2, 'group_order': 5516, 'label': '28A-5', 'order': 28, 'powers': [16, 27, 4, 22], 'representative': 1331, 'size': 197}
  • id: 110602392
    {'aut_label': '28A9', 'centralizer': '197.a1.a1', 'counter': 23, 'group_counter': 2, 'group_order': 5516, 'label': '28A9', 'order': 28, 'powers': [16, 18, 3, 23], 'representative': 4985, 'size': 197}
  • id: 110602393
    {'aut_label': '28A-9', 'centralizer': '197.a1.a1', 'counter': 24, 'group_counter': 2, 'group_order': 5516, 'label': '28A-9', 'order': 28, 'powers': [15, 17, 4, 24], 'representative': 587, 'size': 197}
  • id: 110602394
    {'aut_label': '28A11', 'centralizer': '197.a1.a1', 'counter': 25, 'group_counter': 2, 'group_order': 5516, 'label': '28A11', 'order': 28, 'powers': [14, 21, 4, 25], 'representative': 3019, 'size': 197}
  • id: 110602395
    {'aut_label': '28A-11', 'centralizer': '197.a1.a1', 'counter': 26, 'group_counter': 2, 'group_order': 5516, 'label': '28A-11', 'order': 28, 'powers': [13, 22, 3, 26], 'representative': 1405, 'size': 197}
  • id: 110602396
    {'aut_label': '28A13', 'centralizer': '197.a1.a1', 'counter': 27, 'group_counter': 2, 'group_order': 5516, 'label': '28A13', 'order': 28, 'powers': [12, 25, 3, 27], 'representative': 3601, 'size': 197}
  • id: 110602397
    {'aut_label': '28A-13', 'centralizer': '197.a1.a1', 'counter': 28, 'group_counter': 2, 'group_order': 5516, 'label': '28A-13', 'order': 28, 'powers': [11, 26, 4, 28], 'representative': 935, 'size': 197}
  • id: 110602398
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 29, 'group_counter': 2, 'group_order': 5516, 'label': '197A1', 'order': 197, 'powers': [30, 31, 31, 1], 'representative': 28, 'size': 28}
  • id: 110602400
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 30, 'group_counter': 2, 'group_order': 5516, 'label': '197A2', 'order': 197, 'powers': [32, 29, 29, 1], 'representative': 56, 'size': 28}
  • id: 110602401
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 31, 'group_counter': 2, 'group_order': 5516, 'label': '197A3', 'order': 197, 'powers': [29, 33, 33, 1], 'representative': 84, 'size': 28}
  • id: 110602402
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 32, 'group_counter': 2, 'group_order': 5516, 'label': '197A4', 'order': 197, 'powers': [34, 30, 30, 1], 'representative': 112, 'size': 28}
  • id: 110602403
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 33, 'group_counter': 2, 'group_order': 5516, 'label': '197A5', 'order': 197, 'powers': [31, 35, 35, 1], 'representative': 140, 'size': 28}
  • id: 110602404
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 34, 'group_counter': 2, 'group_order': 5516, 'label': '197A8', 'order': 197, 'powers': [35, 32, 32, 1], 'representative': 224, 'size': 28}
  • id: 110602405
    {'aut_label': '197A1', 'centralizer': '28.a1.a1', 'counter': 35, 'group_counter': 2, 'group_order': 5516, 'label': '197A13', 'order': 197, 'powers': [33, 34, 34, 1], 'representative': 364, 'size': 28}
• 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: 4676925
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.1a', '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], 'schur_index': 1}
  • id: 4676926
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.1b', '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], 'schur_index': 1}
  • id: 4676927
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
  • id: 4676928
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.1d', 'multiplicity': 6, 'nt': [7, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, 6, 6, 6], 'schur_index': 1}
  • id: 4676929
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.1e', 'multiplicity': 6, 'nt': [14, 1], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6], 'schur_index': 1}
  • id: 4676930
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.1f', 'multiplicity': 12, 'nt': [28, 1], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12, 12], 'schur_index': 1}
  • id: 4676931
    {'cdim': 28, 'counter': 7, 'faithful': True, 'group': '5516.b', 'group_order': 5516, 'image': None, 'label': '5516.3.28a', 'multiplicity': 7, 'nt': [197, 0], 'qdim': 196, 'qvalues': [196, 0, 0, 0, 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, -1, -1, -1, -1, -1, -1], '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: 7509836
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 5516, 'label': '5516.3.1a', '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]]]}
  • id: 7509847
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 2758, 'label': '5516.3.1b', '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]]]}
  • id: 7509858
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 1379, 'label': '5516.3.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509865
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 1379, 'label': '5516.3.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509866
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 5, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 788, 'label': '5516.3.1d1', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, -1]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, -2]], [[1, 3]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509867
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 6, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 788, 'label': '5516.3.1d2', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, 1]], [[1, -2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, 2]], [[1, -3]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509868
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 7, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 788, 'label': '5516.3.1d3', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509869
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 8, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 788, 'label': '5516.3.1d4', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509870
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 9, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 788, 'label': '5516.3.1d5', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -3]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -2]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, 3]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509837
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 10, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 788, 'label': '5516.3.1d6', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 3]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 2]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, -3]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509838
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 11, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 394, 'label': '5516.3.1e1', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -3]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, -1]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, -2]], [[-1, 3]], [[-1, 1]], [[-1, -2]], [[-1, 3]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -3]], [[-1, -1]], [[-1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509839
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 12, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 394, 'label': '5516.3.1e2', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, 1]], [[1, -2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 2]], [[-1, -3]], [[-1, -1]], [[-1, 2]], [[-1, -3]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509840
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 13, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 394, 'label': '5516.3.1e3', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, 2]], [[1, -3]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 1]], [[-1, 2]], [[-1, -3]], [[-1, -1]], [[-1, 3]], [[-1, -1]], [[-1, -2]], [[-1, -3]], [[-1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509841
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 14, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 394, 'label': '5516.3.1e4', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, -2]], [[1, 3]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -3]], [[-1, -1]], [[-1, -2]], [[-1, 3]], [[-1, 1]], [[-1, -3]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509842
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 15, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 394, 'label': '5516.3.1e5', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -3]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[-1, -3]], [[-1, 1]], [[-1, -2]], [[-1, -3]], [[-1, 1]], [[-1, 2]], [[-1, 3]], [[-1, -2]], [[-1, 3]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509843
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 16, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1.a1', 'kernel_order': 394, 'label': '5516.3.1e6', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 3]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 3]], [[1, -3]], [[-1, 3]], [[-1, -1]], [[-1, 2]], [[-1, 3]], [[-1, -1]], [[-1, -2]], [[-1, -3]], [[-1, 2]], [[-1, -3]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509844
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 17, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f1', 'nt': [28, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 7]], [[1, 7]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 12]], [[-1, 10]], [[1, 8]], [[-1, 12]], [[1, 2]], [[-1, 4]], [[1, 10]], [[1, 6]], [[-1, 8]], [[-1, 13]], [[-1, 5]], [[1, 11]], [[1, 13]], [[1, 5]], [[-1, 3]], [[-1, 1]], [[-1, 11]], [[1, 1]], [[-1, 9]], [[1, 3]], [[1, 9]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509854
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 26, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f10', 'nt': [28, 12], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 7]], [[-1, 7]], [[1, 4]], [[1, 12]], [[1, 8]], [[-1, 10]], [[-1, 6]], [[-1, 2]], [[1, 10]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 12]], [[1, 2]], [[1, 5]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 3]], [[-1, 13]], [[1, 9]], [[-1, 1]], [[-1, 9]], [[-1, 11]], [[1, 13]], [[1, 11]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509855
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 27, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f11', 'nt': [28, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 7]], [[1, 7]], [[1, 4]], [[1, 12]], [[1, 8]], [[-1, 10]], [[-1, 6]], [[-1, 2]], [[1, 10]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 12]], [[1, 2]], [[-1, 5]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[1, 13]], [[-1, 9]], [[1, 1]], [[1, 9]], [[1, 11]], [[-1, 13]], [[-1, 11]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509856
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 28, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f12', 'nt': [28, 12], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 7]], [[-1, 7]], [[-1, 10]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 8]], [[1, 12]], [[-1, 4]], [[1, 10]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 12]], [[1, 9]], [[-1, 11]], [[1, 13]], [[-1, 9]], [[1, 11]], [[-1, 1]], [[1, 5]], [[-1, 13]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509845
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 18, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f2', 'nt': [28, 12], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 7]], [[-1, 7]], [[1, 12]], [[1, 8]], [[-1, 10]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 2]], [[-1, 12]], [[1, 10]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[1, 1]], [[1, 9]], [[-1, 3]], [[-1, 1]], [[-1, 9]], [[1, 11]], [[1, 13]], [[1, 3]], [[-1, 13]], [[1, 5]], [[-1, 11]], [[-1, 5]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509846
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 19, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f3', 'nt': [28, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 7]], [[1, 7]], [[1, 12]], [[1, 8]], [[-1, 10]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 2]], [[-1, 12]], [[1, 10]], [[-1, 4]], [[-1, 8]], [[1, 6]], [[-1, 1]], [[-1, 9]], [[1, 3]], [[1, 1]], [[1, 9]], [[-1, 11]], [[-1, 13]], [[-1, 3]], [[1, 13]], [[-1, 5]], [[1, 11]], [[1, 5]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509848
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 20, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f4', 'nt': [28, 12], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 7]], [[-1, 7]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 12]], [[-1, 10]], [[1, 8]], [[-1, 12]], [[1, 2]], [[-1, 4]], [[1, 10]], [[1, 6]], [[-1, 8]], [[1, 13]], [[1, 5]], [[-1, 11]], [[-1, 13]], [[-1, 5]], [[1, 3]], [[1, 1]], [[1, 11]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[-1, 9]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509849
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 21, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f5', 'nt': [28, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 7]], [[1, 7]], [[-1, 6]], [[1, 4]], [[1, 12]], [[1, 8]], [[-1, 2]], [[-1, 10]], [[-1, 8]], [[1, 6]], [[-1, 12]], [[1, 2]], [[-1, 4]], [[1, 10]], [[1, 11]], [[-1, 1]], [[-1, 5]], [[-1, 11]], [[1, 1]], [[1, 9]], [[1, 3]], [[1, 5]], [[-1, 3]], [[-1, 13]], [[-1, 9]], [[1, 13]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509850
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 22, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f6', 'nt': [28, 12], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 7]], [[-1, 7]], [[1, 8]], [[-1, 10]], [[-1, 2]], [[-1, 6]], [[1, 12]], [[1, 4]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 12]], [[1, 10]], [[-1, 4]], [[-1, 3]], [[1, 13]], [[1, 9]], [[1, 3]], [[-1, 13]], [[-1, 5]], [[-1, 11]], [[-1, 9]], [[1, 11]], [[1, 1]], [[1, 5]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509851
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 23, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f7', 'nt': [28, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 7]], [[1, 7]], [[1, 8]], [[-1, 10]], [[-1, 2]], [[-1, 6]], [[1, 12]], [[1, 4]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 12]], [[1, 10]], [[-1, 4]], [[1, 3]], [[-1, 13]], [[-1, 9]], [[-1, 3]], [[1, 13]], [[1, 5]], [[1, 11]], [[1, 9]], [[-1, 11]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509852
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 24, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f8', 'nt': [28, 12], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 7]], [[-1, 7]], [[-1, 6]], [[1, 4]], [[1, 12]], [[1, 8]], [[-1, 2]], [[-1, 10]], [[-1, 8]], [[1, 6]], [[-1, 12]], [[1, 2]], [[-1, 4]], [[1, 10]], [[-1, 11]], [[1, 1]], [[1, 5]], [[1, 11]], [[-1, 1]], [[-1, 9]], [[-1, 3]], [[-1, 5]], [[1, 3]], [[1, 13]], [[1, 9]], [[-1, 13]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509853
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5516, 'counter': 25, 'cyclotomic_n': 28, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '28.2', 'image_order': 28, 'indicator': 0, 'kernel': '28.a1.a1', 'kernel_order': 197, 'label': '5516.3.1f9', 'nt': [28, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 7]], [[1, 7]], [[-1, 10]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 8]], [[1, 12]], [[-1, 4]], [[1, 10]], [[1, 6]], [[-1, 8]], [[1, 2]], [[-1, 12]], [[-1, 9]], [[1, 11]], [[-1, 13]], [[1, 9]], [[-1, 11]], [[1, 1]], [[-1, 5]], [[1, 13]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 7509857
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a1', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]], [[1, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]], [[1, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]], [[1, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]], [[1, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]], [[1, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]], [[1, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]]]}
  • id: 7509859
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a2', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]], [[1, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]], [[1, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]], [[1, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]], [[1, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]], [[1, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]], [[1, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]]]}
  • id: 7509860
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a3', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]], [[1, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]], [[1, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]], [[1, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]], [[1, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]], [[1, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]], [[1, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]]]}
  • id: 7509861
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a4', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]], [[1, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]], [[1, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]], [[1, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]], [[1, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]], [[1, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]], [[1, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]]]}
  • id: 7509862
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a5', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]], [[1, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]], [[1, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]], [[1, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]], [[1, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]], [[1, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]], [[1, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]]]}
  • id: 7509863
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a6', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]], [[1, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]], [[1, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]], [[1, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]], [[1, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]], [[1, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]], [[1, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]]]}
  • id: 7509864
    {'center': '5516.a1.a1', 'center_index': 5516, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 197, 'dim': 28, 'faithful': True, 'field': [1163, -1433, -3988, 1348, 217, -84, -1, 1], 'group': '5516.b', 'group_counter': 2, 'group_order': 5516, 'image': None, 'image_isoclass': '5516.b', 'image_order': 5516, 'indicator': 1, 'kernel': '5516.a1.a1', 'kernel_order': 1, 'label': '5516.3.28a7', 'nt': [197, 0], 'q_character': None, 'values': [[[28, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [1, 11], [1, 12], [1, 23], [1, 28], [1, 29], [1, 31], [1, 38], [1, 40], [1, 43], [1, 59], [1, 61], [1, 66], [1, 72], [1, -72], [1, -66], [1, -61], [1, -59], [1, -43], [1, -40], [1, -38], [1, -31], [1, -29], [1, -28], [1, -23], [1, -12], [1, -11], [1, -2]], [[1, 3], [1, 7], [1, 10], [1, 18], [1, 34], [1, 42], [1, 52], [1, 55], [1, 57], [1, 60], [1, 64], [1, 82], [1, 89], [1, 98], [1, -98], [1, -89], [1, -82], [1, -64], [1, -60], [1, -57], [1, -55], [1, -52], [1, -42], [1, -34], [1, -18], [1, -10], [1, -7], [1, -3]], [[1, 13], [1, 15], [1, 16], [1, 27], [1, 35], [1, 50], [1, 51], [1, 63], [1, 74], [1, 78], [1, 88], [1, 90], [1, 94], [1, 96], [1, -96], [1, -94], [1, -90], [1, -88], [1, -78], [1, -74], [1, -63], [1, -51], [1, -50], [1, -35], [1, -27], [1, -16], [1, -15], [1, -13]], [[1, 1], [1, 6], [1, 14], [1, 19], [1, 20], [1, 33], [1, 36], [1, 68], [1, 69], [1, 77], [1, 83], [1, 84], [1, 87], [1, 93], [1, -93], [1, -87], [1, -84], [1, -83], [1, -77], [1, -69], [1, -68], [1, -36], [1, -33], [1, -20], [1, -19], [1, -14], [1, -6], [1, -1]], [[1, 4], [1, 22], [1, 24], [1, 46], [1, 53], [1, 56], [1, 58], [1, 62], [1, 65], [1, 75], [1, 76], [1, 79], [1, 80], [1, 86], [1, -86], [1, -80], [1, -79], [1, -76], [1, -75], [1, -65], [1, -62], [1, -58], [1, -56], [1, -53], [1, -46], [1, -24], [1, -22], [1, -4]], [[1, 5], [1, 9], [1, 17], [1, 21], [1, 26], [1, 30], [1, 32], [1, 41], [1, 49], [1, 54], [1, 70], [1, 71], [1, 95], [1, 97], [1, -97], [1, -95], [1, -71], [1, -70], [1, -54], [1, -49], [1, -41], [1, -32], [1, -30], [1, -26], [1, -21], [1, -17], [1, -9], [1, -5]], [[1, 8], [1, 25], [1, 37], [1, 39], [1, 44], [1, 45], [1, 47], [1, 48], [1, 67], [1, 73], [1, 81], [1, 85], [1, 91], [1, 92], [1, -92], [1, -91], [1, -85], [1, -81], [1, -73], [1, -67], [1, -48], [1, -47], [1, -45], [1, -44], [1, -39], [1, -37], [1, -25], [1, -8]]]}
• 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: 67509896
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5516, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2758, 'label': '5516.b.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5516.b', 'subgroup_hash': 3, 'subgroup_order': 5516, 'subgroup_tex': 'C_{197}:C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 67509900
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2758, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5516.b.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2758.a', 'subgroup_hash': 1, 'subgroup_order': 2758, 'subgroup_tex': 'C_{197}:C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 67509901
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1379, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 1379, 'label': '5516.b.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1379.1', 'subgroup_hash': 1, 'subgroup_order': 1379, 'subgroup_tex': 'C_{197}:C_7', 'supersolvable': True, 'sylow': 0}
  • id: 67509902
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 788, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 394, 'label': '5516.b.7.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '7.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 7, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '788.3', 'subgroup_hash': 3, 'subgroup_order': 788, 'subgroup_tex': 'C_{197}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 67509903
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 394, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5516.b.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '394.1', 'subgroup_hash': 1, 'subgroup_order': 394, 'subgroup_tex': 'D_{197}', 'supersolvable': True, 'sylow': 0}
  • id: 67509904
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 197, 'characteristic': True, 'core_order': 197, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 197, 'label': '5516.b.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{28}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '197.1', 'subgroup_hash': 1, 'subgroup_order': 197, 'subgroup_tex': 'C_{197}', 'supersolvable': True, 'sylow': 197}
  • id: 67509905
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': True, 'direct': None, 'hall': 14, 'label': '5516.b.197.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '197.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 197, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 67509906
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5516.b.394.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '394.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 394, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 67509907
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '5516.b.788.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '788.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 788, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 67509897
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '5516.b.1379.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1379.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1379, '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': 2}
  • id: 67509898
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5516.b.2758.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2758.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2758, '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: 67509899
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5516.b', 'ambient_counter': 2, 'ambient_order': 5516, 'ambient_tex': 'C_{197}:C_{28}', 'central': True, 'central_factor': False, 'centralizer_order': 5516, 'characteristic': True, 'core_order': 1, 'counter': 12, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '5516.b.5516.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5516.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '5516.b', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 5516, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{197}:C_{28}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], '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: 67509896
    {'ambient': '5516.b', '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': '5516.a1.a1', 'complements': ['5516.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '7.a1.a1', '197.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6675, 6957, 2418, 6957, 5884, 5254, 5884, 4746], 'generators': [7, 4, 28, 14], 'label': '5516.b.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '7.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5516.b'}
  • id: 67509897
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '1379.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '197.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '197.a1.a1'], 'contains': ['2758.a1.a1'], 'core': '5516.a1.a1', 'coset_action_label': None, 'count': 197, 'diagramx': [7613, -1, 2468, -1, 8611, -1, 8611, -1], 'generators': [7], 'label': '5516.b.1379.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '197.a1.a1', 'old_label': '1379.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1379.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67509898
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '2758.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '197.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '394.a1.a1', '1379.a1.a1'], 'contains': ['5516.a1.a1'], 'core': '5516.a1.a1', 'coset_action_label': None, 'count': 197, 'diagramx': [4858, -1, 5139, -1, 6465, -1, 6465, -1], 'generators': [14], 'label': '5516.b.2758.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '197.a1.a1', 'old_label': '2758.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2758.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67509899
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '5516.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '788.a1.a1', '2758.a1.a1'], 'contains': [], 'core': '5516.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2528, 3768, 7305, 3768, 4318, 4689, 4318, 5273], 'generators': [], 'label': '5516.b.5516.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '5516.a1.a1', 'normal_contained_in': ['28.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '5516.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5516.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67509900
    {'ambient': '5516.b', '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': '5516.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '14.a1.a1', '394.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3920, 4493, 5164, 4493, 2803, 2580, 2803, 7420], 'generators': [14, 4, 28], 'label': '5516.b.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5516.b'}
  • id: 67509901
    {'ambient': '5516.b', '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': '5516.a1.a1', 'complements': ['1379.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['28.a1.a1', '788.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1563, 1992, 7557, 1992, 1389, 2580, 1389, 7420], 'generators': [4, 28], 'label': '5516.b.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5516.b'}
  • id: 67509902
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5516.a1.a1', 'complements': ['788.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '1379.a1.a1'], 'core': '7.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9034, 8008, 2418, 8008, 8611, 7928, 8611, 2072], 'generators': [7, 14, 28], 'label': '5516.b.7.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '7.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': '7.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5516.b'}
  • id: 67509903
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5516.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '2758.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3522, 4999, 5794, 4999, 6465, 6836, 6465, 3164], 'generators': [14, 28], 'label': '5516.b.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.a1.a1', '7.a1.a1'], 'normal_contains': ['28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5516.b'}
  • id: 67509904
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '28.a1.a1', 'complements': ['197.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1'], 'contains': ['5516.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2102, 3768, 9118, 3768, 4318, 4689, 4318, 5273], 'generators': [28], 'label': '5516.b.28.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['5516.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': '28.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '28.2'}
  • id: 67509905
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '197.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '197.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['394.a1.a1', '1379.a1.a1'], 'core': '5516.a1.a1', 'coset_action_label': None, 'count': 197, 'diagramx': [7244, -1, 882, -1, 5884, -1, 5884, -1], 'generators': [7, 14, 4], 'label': '5516.b.197.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '197.a1.a1', 'old_label': '197.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '197.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67509906
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '394.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '197.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '197.a1.a1'], 'contains': ['788.a1.a1', '2758.a1.a1'], 'core': '5516.a1.a1', 'coset_action_label': None, 'count': 197, 'diagramx': [5823, -1, 4131, -1, 4116, -1, 4116, -1], 'generators': [14, 4], 'label': '5516.b.394.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '197.a1.a1', 'old_label': '394.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '394.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 67509907
    {'ambient': '5516.b', 'aut_centralizer_order': None, 'aut_label': '788.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '197.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '394.a1.a1'], 'contains': ['5516.a1.a1'], 'core': '5516.a1.a1', 'coset_action_label': None, 'count': 197, 'diagramx': [966, -1, 7305, -1, 2172, -1, 2172, -1], 'generators': [4], 'label': '5516.b.788.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '197.a1.a1', 'old_label': '788.a1.a1', 'projective_image': '5516.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '788.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}