Abstract group data - 39732.a

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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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 39732, 'aut_gen_orders': [42, 3], 'aut_gens': [[2305706, 77743], [72595, 201325], [107101, 1721786]], 'aut_group': '79464.b', 'aut_hash': 8542142851885765228, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 79464, 'aut_permdeg': 903, 'aut_perms': [44075647935293851465626311840403304612935205505600868776974253857906737127897128789044361121308973713258604467457797472295851077666311615370952822836348350276668662593698950421146348797805394506869387525026002971726465615911252608871978351222068797631013590111660964006605968941078343719925526989926437370650417645800846560747998599932206840001326286551816381435101824949082743358352536404157222865311892811767888612599172866701616008583108000880831058449510658613380522319698213429417374578783868119935867854567284273065611772388055539291885924894938828431282650940740284967849684446095702875218368260395074299346981039831412769740423571772477168583003643041837695273028055578575679707676871190043390818294841336576946830400778256451510744240051647537339725371112649581847196602930195805958732060320202228410564993592199784953138524411990674228469171189259813784186777624876929228496467955433144721464291705854762234994125618174743637374897788920522955324150298900942847319427869013321191852464304031546154070849459471267959458534419159050969089432899662693555550054566824550145366117282181934483337490053055396298324570529773712696680517083869511589816202924460962371600503940788494897952170831245486911763722377113793083518221802347723024296630933867166959406230780456310178611235457972730794608192526554041998090685669195000649896764048168930687548737390726298188995041513135443581950176733712703082831950248277496856170232637203421163277054529658056470316156363212768015379314366765071023216189419559880630683862200443516310007913816206300064216502556046383829438504942740280212339526697965206382608491234035640278261091483116588555969388651389992280649901896527462114640713040162556817653756119086957908235416441142875510530386927840946374625695482796333683012261751034483844902355705585179839666528525432714522747098559653596027511082954069041295519701689619848749686627321673955424712892209554850214840251579629046162020648106168460384747450114328996130207522464572790908748984899297393798902413410225903147683416519574298223359653377907003288992432356779598942772273628048947632029987456375908738724494890229416813144967992904734326201825943631447078232376565942562999824176583139349999227559498440181860018564063101579065805506479121108144675111147459812045324917264837, 45893240093558223611039975915988859799087711736476552988972343739467841228470363167362033981907949343128294510533807299748157643118442693279285861541751869321647648680775207832075037773807228930351919958405419073637527771364537234471690233812602991116513883545275295808306032807962540693687812119568246188711244958718778525361771174767551880093646779404158816593631218204815424278268237680168064654886346566404700322932356382216978060651703031287040217295089195766132360636481644715977077212638944928094977279900491350503442053131827710578725093329746064482706154546542320819647638610911104331336896014526604079264276528273738483823301246663199499854558068652560432847686954863403948800529425226600791366995327138723526143482705328691496799747692153976000702900888031152571581159749882680852405225703897212874145781322450561575230232688922813680484776723144283684126687515859787312167222352687447429251973067371447822699557857878584018839880910399323718594325593574077386112796446988579554059796986522802301901210018904769772275569623624273701796195775569409731825042980212298772321098023264026732324686959394871636928744554813184409631411945101361053825396799838124982417363502187904514039204790377481155631422078543592357473125849613979393827812916766695830252687980137719153543019284445844749177920802260857602301870768943351870948669753400335647697843183670954178273729310778225813331572402520297645137554486337466564097436913893124802115379801340392710938924096728144102310538598062002158257354616249670100469284969767187435096603553387067112961007838388395406002037532097871760997194121776190535244748369336593891016573004328283990224201567392834549723872116056082437355305830015585547653065832601812503227232066503953900341805446825301489073089172799417947455782919270948307244873503173622469560851436803707176787841411839292086565597027551050903450758299625702198534219999165700406137492862459993437262134579607967312787266551930489121789466735090222299720798334166270618007459802407374217908606014187902096352606244244391504717540191158577204924517745943681622048784950685922078643195943067856213617182223117576462916331181735333231211307200938659468791615373056520810434503117685530505704736088034144953102430203776344681846869493847132026999484714609931193813916507337], 'aut_phi_ratio': 7.883333333333334, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 903, 1, 1], [3, 1892, 1, 1], [7, 1892, 1, 3], [11, 1806, 1, 5], [21, 1892, 1, 6], [22, 1806, 1, 5], [43, 924, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,43)', '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': 39732, 'autcentquo_group': '79464.b', 'autcentquo_hash': 8542142851885765228, 'autcentquo_nilpotent': False, 'autcentquo_order': 79464, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,43)', 'cc_stats': [[1, 1, 1], [2, 903, 1], [3, 1892, 1], [7, 1892, 3], [11, 1806, 5], [21, 1892, 6], [22, 1806, 5], [43, 924, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '39732.a', 'commutator_count': 1, 'commutator_label': '39732.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['39732.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 903, 1, 1], [3, 1892, 1, 1], [7, 1892, 3, 1], [11, 1806, 5, 1], [21, 1892, 6, 1], [22, 1806, 5, 1], [43, 924, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 19380, 'exponent': 19866, 'exponents_of_order': [2, 1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 7, 11, 43], 'factors_of_order': [2, 3, 7, 11, 43], 'faithful_reps': [[21, 0, 2], [42, 1, 10], [43, 1, 1], [44, 1, 10]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '39732.a', 'hash': 6253287762003454422, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 19866, 'inner_gen_orders': [21, 3], 'inner_gens': [[2305706, 63940], [3211727, 77743]], 'inner_hash': 6253287762003454422, 'inner_nilpotent': False, 'inner_order': 39732, 'inner_split': True, 'inner_tex': '\\PSL(2,43)', 'inner_used': [1, 2], 'irrC_degree': 21, 'irrQ_degree': 42, 'irrQ_dim': 42, 'irrR_degree': 42, 'irrep_stats': [[1, 1], [21, 2], [42, 10], [43, 1], [44, 10]], 'label': '39732.a', 'linC_count': 2, 'linC_degree': 21, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 42, 'linQ_degree_count': 1, 'linQ_dim': 42, 'linQ_dim_count': 1, 'linR_count': 11, 'linR_degree': 42, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,43)', '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, 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': 23, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 24, 'number_divisions': 8, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 19, 'number_subgroup_classes': 20, 'number_subgroups': 25462, 'old_label': None, 'order': 39732, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 903], [3, 1892], [7, 5676], [11, 9030], [21, 11352], [22, 9030], [43, 1848]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [3062686], 'outer_gens': [[1586713, 35560]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 44, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [42, 1], [43, 1], [44, 1], [132, 1], [210, 2], [264, 1]], 'representations': {'Lie': [{'d': 2, 'q': 43, 'gens': [77743, 2305706], 'family': 'PSL'}, {'d': 2, 'q': 43, 'family': 'PSU'}, {'d': 3, 'q': 43, 'family': 'Omega'}, {'d': 3, 'q': 43, 'family': 'POmega'}, {'d': 2, 'q': 43, 'family': 'PSigmaL'}], 'Perm': {'d': 44, 'gens': [84097220283574540833463266472729272952958918168177, 2598723221027585877916762490227752448646954838780493047]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,43)', 'transitive_degree': 44, '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: 175096987
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 39732, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1, 1, 1], 'representative': 79508, 'size': 1}
  • id: 175096998
    {'aut_label': '2A', 'centralizer': '903.a1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 39732, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2, 2, 2], 'representative': 2258160, 'size': 903}
  • id: 175097004
    {'aut_label': '3A', 'centralizer': '1892.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 39732, 'label': '3A', 'order': 3, 'powers': [3, 1, 3, 3, 3, 3], 'representative': 2111144, 'size': 1892}
  • id: 175097005
    {'aut_label': '7A1', 'centralizer': '1892.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 39732, 'label': '7A1', 'order': 7, 'powers': [5, 6, 5, 1, 6, 4], 'representative': 3417875, 'size': 1892}
  • id: 175097006
    {'aut_label': '7A2', 'centralizer': '1892.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 39732, 'label': '7A2', 'order': 7, 'powers': [6, 4, 6, 1, 4, 5], 'representative': 1626612, 'size': 1892}
  • id: 175097007
    {'aut_label': '7A3', 'centralizer': '1892.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 39732, 'label': '7A3', 'order': 7, 'powers': [4, 5, 4, 1, 5, 6], 'representative': 2812673, 'size': 1892}
  • id: 175097008
    {'aut_label': '11A1', 'centralizer': '1806.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 39732, 'label': '11A1', 'order': 11, 'powers': [8, 9, 11, 10, 1, 7], 'representative': 2056798, 'size': 1806}
  • id: 175097009
    {'aut_label': '11A2', 'centralizer': '1806.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 39732, 'label': '11A2', 'order': 11, 'powers': [10, 11, 7, 9, 1, 8], 'representative': 1069626, 'size': 1806}
  • id: 175097010
    {'aut_label': '11A3', 'centralizer': '1806.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 39732, 'label': '11A3', 'order': 11, 'powers': [11, 8, 10, 7, 1, 9], 'representative': 2219900, 'size': 1806}
  • id: 175096988
    {'aut_label': '11A4', 'centralizer': '1806.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 39732, 'label': '11A4', 'order': 11, 'powers': [9, 7, 8, 11, 1, 10], 'representative': 731916, 'size': 1806}
  • id: 175096989
    {'aut_label': '11A5', 'centralizer': '1806.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 39732, 'label': '11A5', 'order': 11, 'powers': [7, 10, 9, 8, 1, 11], 'representative': 2716627, 'size': 1806}
  • id: 175096990
    {'aut_label': '21A1', 'centralizer': '1892.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 39732, 'label': '21A1', 'order': 21, 'powers': [13, 4, 15, 3, 17, 12], 'representative': 2607827, 'size': 1892}
  • id: 175096991
    {'aut_label': '21A2', 'centralizer': '1892.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 39732, 'label': '21A2', 'order': 21, 'powers': [14, 5, 17, 3, 12, 13], 'representative': 2621870, 'size': 1892}
  • id: 175096992
    {'aut_label': '21A4', 'centralizer': '1892.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 39732, 'label': '21A4', 'order': 21, 'powers': [16, 6, 12, 3, 13, 14], 'representative': 2948312, 'size': 1892}
  • id: 175096993
    {'aut_label': '21A5', 'centralizer': '1892.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 39732, 'label': '21A5', 'order': 21, 'powers': [17, 5, 14, 3, 16, 15], 'representative': 2519910, 'size': 1892}
  • id: 175096994
    {'aut_label': '21A8', 'centralizer': '1892.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 39732, 'label': '21A8', 'order': 21, 'powers': [15, 4, 13, 3, 14, 16], 'representative': 1926902, 'size': 1892}
  • id: 175096995
    {'aut_label': '21A10', 'centralizer': '1892.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 39732, 'label': '21A10', 'order': 21, 'powers': [12, 6, 16, 3, 15, 17], 'representative': 2154200, 'size': 1892}
  • id: 175096996
    {'aut_label': '22A1', 'centralizer': '1806.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 39732, 'label': '22A1', 'order': 22, 'powers': [7, 19, 20, 21, 2, 18], 'representative': 1662247, 'size': 1806}
  • id: 175096997
    {'aut_label': '22A3', 'centralizer': '1806.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 39732, 'label': '22A3', 'order': 22, 'powers': [9, 22, 21, 18, 2, 19], 'representative': 2677227, 'size': 1806}
  • id: 175096999
    {'aut_label': '22A5', 'centralizer': '1806.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 39732, 'label': '22A5', 'order': 22, 'powers': [11, 21, 19, 22, 2, 20], 'representative': 1374303, 'size': 1806}
  • id: 175097000
    {'aut_label': '22A7', 'centralizer': '1806.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 39732, 'label': '22A7', 'order': 22, 'powers': [10, 18, 22, 20, 2, 21], 'representative': 2244805, 'size': 1806}
  • id: 175097001
    {'aut_label': '22A9', 'centralizer': '1806.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 39732, 'label': '22A9', 'order': 22, 'powers': [8, 20, 18, 19, 2, 22], 'representative': 17484, 'size': 1806}
  • id: 175097002
    {'aut_label': '43A1', 'centralizer': '924.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 39732, 'label': '43A1', 'order': 43, 'powers': [24, 24, 24, 24, 23, 1], 'representative': 242089, 'size': 924}
  • id: 175097003
    {'aut_label': '43A1', 'centralizer': '924.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 39732, 'label': '43A-1', 'order': 43, 'powers': [23, 23, 23, 23, 24, 1], 'representative': 83073, 'size': 924}
• 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: 18182072
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.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], 'schur_index': 1}
  • id: 18182073
    {'cdim': 21, 'counter': 2, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.21a', 'multiplicity': 2, 'nt': [903, 0], 'qdim': 42, 'qvalues': [42, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, -1], 'schur_index': 1}
  • id: 18182076
    {'cdim': 43, 'counter': 5, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.43a', 'multiplicity': 1, 'nt': [44, 233], 'qdim': 43, 'qvalues': [43, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 18182077
    {'cdim': 44, 'counter': 6, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.44a', 'multiplicity': 1, 'nt': [132, 0], 'qdim': 44, 'qvalues': [44, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 18182078
    {'cdim': 44, 'counter': 7, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.44b', 'multiplicity': 3, 'nt': [308, 0], 'qdim': 132, 'qvalues': [132, 0, 6, -1, -1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 3, 3], 'schur_index': 1}
  • id: 18182074
    {'cdim': 42, 'counter': 3, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.42a', 'multiplicity': 5, 'nt': [903, 0], 'qdim': 210, 'qvalues': [210, 10, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -5, -5], 'schur_index': 1}
  • id: 18182075
    {'cdim': 42, 'counter': 4, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.42b', 'multiplicity': 5, 'nt': [1806, 0], 'qdim': 210, 'qvalues': [210, -10, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -5, -5], 'schur_index': 1}
  • id: 18182079
    {'cdim': 44, 'counter': 8, 'faithful': True, 'group': '39732.a', 'group_order': 39732, 'image': None, 'label': '39732.a.44c', 'multiplicity': 6, 'nt': [903, 0], 'qdim': 264, 'qvalues': [264, 0, -6, -2, -2, -2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 6, 6], '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: 39294772
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 39732, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 39732, 'label': '39732.a.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]]]}
  • id: 39294783
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 2, 'cyclotomic_n': 43, 'dim': 21, 'faithful': True, 'field': [11, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 0, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.21a1', 'nt': [903, 0], 'q_character': None, 'values': [[[21, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-1, 1], [-1, 4], [-1, 6], [-1, 9], [-1, 10], [-1, 11], [-1, 13], [-1, 14], [-1, 15], [-1, 16], [-1, 17], [-1, 21], [-1, -20], [-1, -19], [-1, -18], [-1, -12], [-1, -8], [-1, -7], [-1, -5], [-1, -3], [-1, -2]], [[1, 1], [1, 4], [1, 6], [1, 9], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 21], [1, -20], [1, -19], [1, -18], [1, -12], [1, -8], [1, -7], [1, -5], [1, -3], [1, -2]]]}
  • id: 39294789
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 43, 'dim': 21, 'faithful': True, 'field': [11, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 0, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.21a2', 'nt': [903, 2], 'q_character': None, 'values': [[[21, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1], [1, 4], [1, 6], [1, 9], [1, 10], [1, 11], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 21], [1, -20], [1, -19], [1, -18], [1, -12], [1, -8], [1, -7], [1, -5], [1, -3], [1, -2]], [[-1, 0], [-1, 1], [-1, 4], [-1, 6], [-1, 9], [-1, 10], [-1, 11], [-1, 13], [-1, 14], [-1, 15], [-1, 16], [-1, 17], [-1, 21], [-1, -20], [-1, -19], [-1, -18], [-1, -12], [-1, -8], [-1, -7], [-1, -5], [-1, -3], [-1, -2]]]}
  • id: 39294790
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42a1', 'nt': [903, 0], 'q_character': None, 'values': [[[42, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294791
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42a2', 'nt': [903, 0], 'q_character': None, 'values': [[[42, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294792
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42a3', 'nt': [903, 0], 'q_character': None, 'values': [[[42, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294793
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42a4', 'nt': [903, 0], 'q_character': None, 'values': [[[42, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294794
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42a5', 'nt': [903, 0], 'q_character': None, 'values': [[[42, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294795
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42b1', 'nt': [1806, 0], 'q_character': None, 'values': [[[42, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294773
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42b2', 'nt': [1806, 0], 'q_character': None, 'values': [[[42, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294774
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42b3', 'nt': [1806, 0], 'q_character': None, 'values': [[[42, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294775
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42b4', 'nt': [1806, 0], 'q_character': None, 'values': [[[42, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294776
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 11, 'dim': 42, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.42b5', 'nt': [1806, 0], 'q_character': None, 'values': [[[42, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 0]], [[-1, 0]]]}
  • id: 39294777
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 1, 'dim': 43, 'faithful': True, 'field': [0, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.43a', 'nt': [44, 233], 'q_character': None, 'values': [[[43, 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]], [[0, 0]], [[0, 0]]]}
  • id: 39294778
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 1, 'dim': 44, 'faithful': True, 'field': [0, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44a', 'nt': [132, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294779
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 7, 'dim': 44, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44b1', 'nt': [308, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294780
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 7, 'dim': 44, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44b2', 'nt': [308, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294781
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 7, 'dim': 44, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44b3', 'nt': [308, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294782
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 21, 'dim': 44, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44c1', 'nt': [903, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 10], [1, -10]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 8], [1, -8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294784
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 21, 'dim': 44, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44c2', 'nt': [903, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 10], [1, -10]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 8], [1, -8]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294785
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 21, 'dim': 44, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44c3', 'nt': [903, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 8], [1, -8]], [[1, 10], [1, -10]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294786
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 21, 'dim': 44, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44c4', 'nt': [903, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 8], [1, -8]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 10], [1, -10]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294787
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 21, 'dim': 44, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44c5', 'nt': [903, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[1, 1], [1, -1]], [[1, 10], [1, -10]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 39294788
    {'center': '39732.a1.a1', 'center_index': 39732, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 21, 'dim': 44, 'faithful': True, 'field': [1, -8, 8, 6, -6, -1, 1], 'group': '39732.a', 'group_counter': 1, 'group_order': 39732, 'image': None, 'image_isoclass': '39732.a', 'image_order': 39732, 'indicator': 1, 'kernel': '39732.a1.a1', 'kernel_order': 1, 'label': '39732.a.44c6', 'nt': [903, 0], 'q_character': None, 'values': [[[44, 0]], [[0, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 9], [1, -9]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 8], [1, -8]], [[1, 4], [1, -4]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 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: 269907337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 39732, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 19866, 'label': '39732.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '39732.a', 'subgroup_hash': 6253287762003454422, 'subgroup_order': 39732, 'subgroup_tex': '\\PSL(2,43)', 'supersolvable': False, 'sylow': 0}
  • id: 269907348
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 903, 'label': '39732.a.44.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, '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': '903.1', 'subgroup_hash': 1, 'subgroup_order': 903, 'subgroup_tex': 'C_{43}:C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 269907350
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 301, 'label': '39732.a.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, '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': '301.1', 'subgroup_hash': 1, 'subgroup_order': 301, 'subgroup_tex': 'C_{43}:C_7', 'supersolvable': True, 'sylow': 0}
  • id: 269907351
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 129, 'label': '39732.a.308.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '308.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': 308, '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': '129.1', 'subgroup_hash': 1, 'subgroup_order': 129, 'subgroup_tex': 'C_{43}:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 269907352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 22, 'label': '39732.a.903.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '903.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': 903, '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 269907353
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 43, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': True, 'direct': None, 'hall': 43, 'label': '39732.a.924.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '924.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': 924, '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': '43.1', 'subgroup_hash': 1, 'subgroup_order': 43, 'subgroup_tex': 'C_{43}', 'supersolvable': True, 'sylow': 43}
  • id: 269907354
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '39732.a.946.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '946.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': 946, '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': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 269907355
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '39732.a.1806.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1806.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': 1806, '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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 269907356
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '39732.a.1806.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1806.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1806, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 269907338
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '39732.a.1806.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1806.b1.a2', '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': 1806, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 269907339
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 21, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 21, 'label': '39732.a.1892.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1892.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': 1892, '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': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
  • id: 269907340
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '39732.a.2838.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2838.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': 2838, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 269907341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '39732.a.3311.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3311.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': 3311, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 269907342
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 11, 'label': '39732.a.3612.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3612.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': 3612, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
  • id: 269907343
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 21, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '39732.a.5676.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5676.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': 5676, '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: 269907344
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '39732.a.6622.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6622.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': 6622, '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: 269907345
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '39732.a.9933.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9933.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': 9933, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 269907346
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 21, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '39732.a.13244.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13244.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': 13244, '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': 3}
  • id: 269907347
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '39732.a.19866.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '19866.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': 19866, '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: 269907349
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '39732.a', 'ambient_counter': 1, 'ambient_order': 39732, 'ambient_tex': '\\PSL(2,43)', 'central': True, 'central_factor': False, 'centralizer_order': 39732, 'characteristic': True, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '39732.a.39732.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '39732.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '39732.a', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6253287762003454422, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 39732, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,43)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C1'], '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: 269907337
    {'ambient': '39732.a', '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': '39732.a1.a1', 'complements': ['39732.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['44.a1.a1', '903.a1.a1', '946.a1.a1', '3311.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5671, 5000, 5243, 5000, 5860, 5000, 5238, 5000], 'generators': [140951, 2795825], 'label': '39732.a.1.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['39732.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '39732.a', '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': '39732.a'}
  • id: 269907338
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '1806.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19866.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['903.a1.a1'], 'contains': ['3612.a1.a1', '19866.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 903, 'diagramx': [8149, -1, 8371, -1, 9526, -1, 9577, -1], 'generators': [2184889, 238118], 'label': '39732.a.1806.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '903.a1.a1', 'old_label': '1806.b1.a2', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1806.b1.a2', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 269907339
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '1892.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1892.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1.a1', '946.a1.a1'], 'contains': ['5676.a1.a1', '13244.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 946, 'diagramx': [2612, -1, 3364, -1, 3647, -1, 3260, -1], 'generators': [2027037, 2861454], 'label': '39732.a.1892.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '946.a1.a1', 'old_label': '1892.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1892.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269907340
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '2838.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['946.a1.a1'], 'contains': ['5676.a1.a1', '19866.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 2838, 'diagramx': [4417, -1, 4140, -1, 4713, -1, 4213, -1], 'generators': [1573918, 1464046], 'label': '39732.a.2838.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2838.a1.a1', 'old_label': '2838.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2838.a1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
  • id: 269907341
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '3311.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9933.a1.a1', '13244.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 3311, 'diagramx': [6074, -1, 5585, -1, 6406, -1, 5727, -1], 'generators': [3395625, 621301, 3409944], 'label': '39732.a.3311.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3311.a1.a1', 'old_label': '3311.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3311.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 269907342
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '3612.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1806.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1806.a1.a1', '1806.b1.a1', '1806.b1.a2'], 'contains': ['39732.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 903, 'diagramx': [9299, -1, 8568, -1, 8340, -1, 7980, -1], 'generators': [238118], 'label': '39732.a.3612.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '903.a1.a1', 'old_label': '3612.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3612.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269907343
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '5676.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1892.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.a1.a1', '1892.a1.a1', '2838.a1.a1'], 'contains': ['39732.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 946, 'diagramx': [2194, -1, 2667, -1, 4047, -1, 3498, -1], 'generators': [423779], 'label': '39732.a.5676.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '946.a1.a1', 'old_label': '5676.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5676.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269907344
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '6622.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['946.a1.a1'], 'contains': ['13244.a1.a1', '19866.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 6622, 'diagramx': [5238, -1, 4140, -1, 5673, -1, 5071, -1], 'generators': [1464046, 1075201], 'label': '39732.a.6622.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6622.a1.a1', 'old_label': '6622.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6622.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 269907345
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '9933.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9933.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['903.a1.a1', '3311.a1.a1'], 'contains': ['19866.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 3311, 'diagramx': [6895, -1, 6203, -1, 7206, -1, 6442, -1], 'generators': [2184889, 3384746], 'label': '39732.a.9933.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3311.a1.a1', 'old_label': '9933.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9933.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 269907346
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '13244.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1892.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['308.a1.a1', '1892.a1.a1', '3311.a1.a1', '6622.a1.a1'], 'contains': ['39732.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 946, 'diagramx': [4015, -1, 3731, -1, 5060, -1, 4833, -1], 'generators': [2027037], 'label': '39732.a.13244.a1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '946.a1.a1', 'old_label': '13244.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13244.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269907347
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '19866.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '903.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1806.a1.a1', '1806.b1.a1', '1806.b1.a2', '2838.a1.a1', '6622.a1.a1', '9933.a1.a1'], 'contains': ['39732.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 903, 'diagramx': [6358, -1, 6203, -1, 6433, -1, 6442, -1], 'generators': [2184889], 'label': '39732.a.19866.a1.a1', 'mobius_quo': None, 'mobius_sub': 22, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '903.a1.a1', 'old_label': '19866.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '19866.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269907348
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['132.a1.a1', '308.a1.a1', '1892.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': '44T233', 'count': 44, 'diagramx': [3388, -1, 2943, -1, 3007, -1, 2688, -1], 'generators': [2027037, 2005622, 2861454], 'label': '39732.a.44.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '903.1'}
  • id: 269907349
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '39732.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': ['924.a1.a1', '3612.a1.a1', '5676.a1.a1', '13244.a1.a1', '19866.a1.a1'], 'contains': [], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4015, 5000, 3731, 5000, 5060, 5000, 4833, 5000], 'generators': [], 'label': '39732.a.39732.a1.a1', 'mobius_quo': 1, 'mobius_sub': -39732, 'normal_closure': '39732.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '39732.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '39732.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 269907350
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1.a1'], 'contains': ['924.a1.a1', '5676.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [1462, -1, 1157, -1, 673, -1, 602, -1], 'generators': [2005622, 423779], 'label': '39732.a.132.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '903.1'}
  • id: 269907351
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '308.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1.a1'], 'contains': ['924.a1.a1', '13244.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [2642, -1, 2195, -1, 2260, -1, 2020, -1], 'generators': [2027037, 2005622], 'label': '39732.a.308.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '308.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '308.a1.a1', 'subgroup_fusion': None, 'weyl_group': '903.1'}
  • id: 269907352
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '903.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19866.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['1806.a1.a1', '1806.b1.a1', '1806.b1.a2', '9933.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 903, 'diagramx': [7582, -1, 7201, -1, 7913, -1, 7455, -1], 'generators': [2184889, 238118, 3384746], 'label': '39732.a.903.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '903.a1.a1', 'old_label': '903.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '903.a1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 269907353
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '924.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '924.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.a1.a1', '308.a1.a1'], 'contains': ['39732.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [523, -1, 460, -1, 2260, -1, 2020, -1], 'generators': [2005622], 'label': '39732.a.924.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '924.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '924.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.2'}
  • id: 269907354
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '946.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39732.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['1892.a1.a1', '2838.a1.a1', '6622.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 946, 'diagramx': [4850, -1, 4468, -1, 5020, -1, 4487, -1], 'generators': [1573918, 1464046, 1075201], 'label': '39732.a.946.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '946.a1.a1', 'old_label': '946.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '946.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.5'}
  • id: 269907355
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '1806.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1806.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['903.a1.a1'], 'contains': ['3612.a1.a1', '19866.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 903, 'diagramx': [9477, -1, 9540, -1, 8340, -1, 7455, -1], 'generators': [238118, 3384746], 'label': '39732.a.1806.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '903.a1.a1', 'old_label': '1806.a1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1806.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 269907356
    {'ambient': '39732.a', 'aut_centralizer_order': None, 'aut_label': '1806.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '19866.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['903.a1.a1'], 'contains': ['3612.a1.a1', '19866.a1.a1'], 'core': '39732.a1.a1', 'coset_action_label': None, 'count': 903, 'diagramx': [8149, -1, 7201, -1, 9526, -1, 8516, -1], 'generators': [37625, 238118], 'label': '39732.a.1806.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '903.a1.a1', 'old_label': '1806.b1.a1', 'projective_image': '39732.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1806.b1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}