Abstract group data - 2420.r

Formats: - HTML - YAML - JSON - 2025-11-17T21:32:21.667851

• 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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 10, 22, 22], 'aut_gens': [[1, 10, 110], [9, 1100, 1300], [61, 90, 1870], [711, 100, 110], [1261, 10, 110]], 'aut_group': '48400.l', 'aut_hash': 3341594860267235989, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48400, 'aut_permdeg': 484, 'aut_perms': [62520099086582945224664738411832045921631117340072713023410331171451972391305739211927452306870660446505355277483462481638849072450791982278665724617547577985188973685207453616552422435613290706898056489276060654705207441225118335366155093990023351107720108830179793079403782633405937515252324422315515051993274874334259286815799887682190875754118486036801038965379387627182866938537985448137043401077991826199740356650900961704965721815086264026973261117586885883894924067755952848981710206357373228113876312806188729344189538347183903010580693628471111080838724161173110901441635553845356263867970752726790360077580871148453732795491814700464064451083894753680006832863039516835323428371613295635435776152500722970780515996679588658419319448209866277785878523392508065373425886450708852410851476312071009548385808084219612877246107598223646888730339821707356951711229810819277908248078950506376099671964994962613003683753131828457740922488813271407757387583519022553323789169707539593038734684905040691854057689541563560365655040076915956105658092613633028216000747973252093433099335100659, 58545762571423547493642474770586878489741176112508464630106739859275516496440451824418444435402875690761132381321487802980209733820092314970817251013309579520563078738464174764269820279314568499290010398034252246201749982697887326979359242860159017742200822275079795235220767051772439307441980325581610170994407548884819747499206013703618110770615058455094553958256844772872503148579857899798250773744320896598568631763544691891878322153731328497390823586582772451727968981641537366627130433469368066529568018918325606030140033450938351742121699170139271692190461919539847973954750627381140813295310842518061334767923344638147827502127581102411203141604031799092090295924793096714300606322605777227781378908440888512833662771253789472692817098361617198201294671907529481662465305716534842058541990595098981773776763526513824144474834988858919414187983634309103165571421134040963316480983043092108907227359518177615237757210921922288667927147768502323048557379319753364009978489340516087230624031420203616258287880952416357042971210815433410579915776305367425115798565739799486963644608321683, 9525733051992548275726466967551101922846700992630997132956032472406050691238973022609770540699387046772386910188520664113734949300276573237224030396747849716444124420601654335021460402631730379142469751309832822511090363840815658714011058338926325861427001926824964120929965164958621681730837036595391761939290846226662845701093299884789272999789743336099575548014998211184261256450602327407555218128147029491529630367320660524985851709325080362628104375941402453611939117794707961038730113299902629573747581766850631135869439650263414536455643206787654314900917137557077488728597954972006828147024625763952842642004273312945926068392890902719711197549172270627022307511492070329149852439048950454776132969344246556911291227072078718326352704958971552418842272038549621113356092027078594309041709234482359809571257942497113410850164717906815868663279755721092353678481804051155043683461509349039482686572267780074409575615481338415254929083515293798625544261505312653651034607263882152342620633470169409918114799286404193036742488946555644833502919551624106032038220003715904389434529904874, 28705869740709713601502419771555517175209060056855865138982252546225426857126412797374400386111640014908661469506672377644342365016029740267044935806253593951467195724579028752119686914501787122740342993575568015467602992044541292931377748802854147457693347777941426352935072154453363635486771594311376534690396034896892748492358738743446896634998645116259032829941678192100979313886372089138966580604083760739658969940510185809298276351481807222579766109291079506293368058040640119536055163380740908980563622198035824245414246027473400446036629486015757327722468666661148452620440568915510783905467586432966033419413024569418170366620769107080880174281057816393190441391840966537364225114760469963479339529149321792305960291369776381038805091233445785586446422721240125565506588636864611734333581444734097434929933425294351647924769301622076969461916245867838631099410430309377407897308997382203049361860495513873069912804883428533917834026738696333937089198782077551651230678488937579413390779901808255211325410658972596831291640588391911876521088135367477666646538549384283956452721640754], 'aut_phi_ratio': 55.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 2, 1], [5, 121, 2, 2], [10, 121, 2, 2], [10, 121, 4, 2], [11, 10, 2, 1], [11, 10, 10, 1], [22, 10, 2, 1], [22, 10, 10, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{11}^2:C_2^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [5, 121, 4], [10, 121, 12], [11, 10, 12], [22, 10, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '1210.10', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '11.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 18, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1210.10', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [5, 121, 4, 1], [10, 121, 4, 3], [11, 10, 1, 2], [11, 10, 5, 2], [22, 10, 1, 2], [22, 10, 5, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 110, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 10]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2420.r', 'hash': 2157492669750725759, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11, 11], 'inner_gens': [[1, 70, 2090], [51, 10, 110], [441, 10, 110]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 1210, 'inner_split': False, 'inner_tex': 'C_{11}:F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 10, 'irrQ_degree': 50, 'irrQ_dim': 50, 'irrR_degree': 10, 'irrep_stats': [[1, 20], [10, 24]], 'label': '2420.r', 'linC_count': 10, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 3, 'linQ_dim': 20, 'linQ_dim_count': 3, 'linR_count': 10, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C22:F11', 'ngens': 5, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 44, 'number_divisions': 16, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 50, 'number_subgroups': 1510, 'old_label': None, 'order': 2420, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 243], [5, 484], [10, 1452], [11, 120], [22, 120]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10], 'outer_gen_pows': [0, 6, 0], 'outer_gens': [[9, 220, 1270], [1211, 20, 1870], [1, 20, 110]], 'outer_group': '40.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 11, 'outer_perms': [3629520, 41040, 766], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4], [10, 4], [50, 4]], 'representations': {'PC': {'code': '6372473303491881090677902743303909', 'gens': [1, 3, 4], 'pres': [5, -2, -5, -11, -2, -11, 10, 1052, 382, 41803, 9908, 58, 44004, 24759]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [13240838059471336, 13669369333096837, 20595883671717277, 32182222080390795, 41772741070013040]}, 'Perm': {'d': 24, 'gens': [479001600, 10540080640000325105282, 38777365, 262160289644134033152000, 1129232178557701308856]}}, 'schur_multiplier': [22], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{22}:F_{11}', 'transitive_degree': 110, '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: 109385582
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 18, 'group_order': 2420, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 109385593
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 18, 'group_order': 2420, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 1210, 'size': 1}
  • id: 109385604
    {'aut_label': '2B', 'centralizer': '121.a1.a1', 'counter': 3, 'group_counter': 18, 'group_order': 2420, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 2065, 'size': 121}
  • id: 109385615
    {'aut_label': '2B', 'centralizer': '121.a1.a1', 'counter': 4, 'group_counter': 18, 'group_order': 2420, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 595, 'size': 121}
  • id: 109385621
    {'aut_label': '5A1', 'centralizer': '121.a1.a1', 'counter': 5, 'group_counter': 18, 'group_order': 2420, 'label': '5A1', 'order': 5, 'powers': [7, 1, 5], 'representative': 546, 'size': 121}
  • id: 109385622
    {'aut_label': '5A1', 'centralizer': '121.a1.a1', 'counter': 6, 'group_counter': 18, 'group_order': 2420, 'label': '5A-1', 'order': 5, 'powers': [8, 1, 6], 'representative': 694, 'size': 121}
  • id: 109385623
    {'aut_label': '5A2', 'centralizer': '121.a1.a1', 'counter': 7, 'group_counter': 18, 'group_order': 2420, 'label': '5A2', 'order': 5, 'powers': [6, 1, 7], 'representative': 1822, 'size': 121}
  • id: 109385624
    {'aut_label': '5A2', 'centralizer': '121.a1.a1', 'counter': 8, 'group_counter': 18, 'group_order': 2420, 'label': '5A-2', 'order': 5, 'powers': [5, 1, 8], 'representative': 898, 'size': 121}
  • id: 109385625
    {'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 9, 'group_counter': 18, 'group_order': 2420, 'label': '10A1', 'order': 10, 'powers': [5, 3, 9], 'representative': 1173, 'size': 121}
  • id: 109385583
    {'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 10, 'group_counter': 18, 'group_order': 2420, 'label': '10A-1', 'order': 10, 'powers': [6, 3, 10], 'representative': 247, 'size': 121}
  • id: 109385584
    {'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 11, 'group_counter': 18, 'group_order': 2420, 'label': '10A3', 'order': 10, 'powers': [8, 3, 11], 'representative': 1379, 'size': 121}
  • id: 109385585
    {'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 12, 'group_counter': 18, 'group_order': 2420, 'label': '10A-3', 'order': 10, 'powers': [7, 3, 12], 'representative': 1631, 'size': 121}
  • id: 109385586
    {'aut_label': '10B1', 'centralizer': '121.a1.a1', 'counter': 13, 'group_counter': 18, 'group_order': 2420, 'label': '10B1', 'order': 10, 'powers': [5, 2, 13], 'representative': 368, 'size': 121}
  • id: 109385587
    {'aut_label': '10B1', 'centralizer': '121.a1.a1', 'counter': 14, 'group_counter': 18, 'group_order': 2420, 'label': '10B-1', 'order': 10, 'powers': [6, 2, 14], 'representative': 1942, 'size': 121}
  • id: 109385588
    {'aut_label': '10B3', 'centralizer': '121.a1.a1', 'counter': 15, 'group_counter': 18, 'group_order': 2420, 'label': '10B3', 'order': 10, 'powers': [8, 2, 15], 'representative': 644, 'size': 121}
  • id: 109385589
    {'aut_label': '10B3', 'centralizer': '121.a1.a1', 'counter': 16, 'group_counter': 18, 'group_order': 2420, 'label': '10B-3', 'order': 10, 'powers': [7, 2, 16], 'representative': 856, 'size': 121}
  • id: 109385590
    {'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 17, 'group_counter': 18, 'group_order': 2420, 'label': '10C1', 'order': 10, 'powers': [6, 4, 17], 'representative': 347, 'size': 121}
  • id: 109385591
    {'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 18, 'group_counter': 18, 'group_order': 2420, 'label': '10C-1', 'order': 10, 'powers': [5, 4, 18], 'representative': 1743, 'size': 121}
  • id: 109385592
    {'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 19, 'group_counter': 18, 'group_order': 2420, 'label': '10C3', 'order': 10, 'powers': [7, 4, 19], 'representative': 2411, 'size': 121}
  • id: 109385594
    {'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 20, 'group_counter': 18, 'group_order': 2420, 'label': '10C-3', 'order': 10, 'powers': [8, 4, 20], 'representative': 859, 'size': 121}
  • id: 109385595
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 21, 'group_counter': 18, 'group_order': 2420, 'label': '11A', 'order': 11, 'powers': [21, 21, 1], 'representative': 220, 'size': 10}
  • id: 109385596
    {'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 22, 'group_counter': 18, 'group_order': 2420, 'label': '11B', 'order': 11, 'powers': [22, 22, 1], 'representative': 20, 'size': 10}
  • id: 109385597
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 23, 'group_counter': 18, 'group_order': 2420, 'label': '11C1', 'order': 11, 'powers': [24, 27, 1], 'representative': 240, 'size': 10}
  • id: 109385598
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 24, 'group_counter': 18, 'group_order': 2420, 'label': '11C2', 'order': 11, 'powers': [26, 23, 1], 'representative': 480, 'size': 10}
  • id: 109385599
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 25, 'group_counter': 18, 'group_order': 2420, 'label': '11C3', 'order': 11, 'powers': [27, 26, 1], 'representative': 720, 'size': 10}
  • id: 109385600
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 26, 'group_counter': 18, 'group_order': 2420, 'label': '11C4', 'order': 11, 'powers': [25, 24, 1], 'representative': 960, 'size': 10}
  • id: 109385601
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 27, 'group_counter': 18, 'group_order': 2420, 'label': '11C5', 'order': 11, 'powers': [23, 25, 1], 'representative': 1200, 'size': 10}
  • id: 109385602
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 28, 'group_counter': 18, 'group_order': 2420, 'label': '11D1', 'order': 11, 'powers': [29, 32, 1], 'representative': 260, 'size': 10}
  • id: 109385603
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 29, 'group_counter': 18, 'group_order': 2420, 'label': '11D2', 'order': 11, 'powers': [31, 28, 1], 'representative': 520, 'size': 10}
  • id: 109385605
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 30, 'group_counter': 18, 'group_order': 2420, 'label': '11D3', 'order': 11, 'powers': [32, 31, 1], 'representative': 670, 'size': 10}
  • id: 109385606
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 31, 'group_counter': 18, 'group_order': 2420, 'label': '11D4', 'order': 11, 'powers': [30, 29, 1], 'representative': 930, 'size': 10}
  • id: 109385607
    {'aut_label': '11C1', 'centralizer': '10.a1.a1', 'counter': 32, 'group_counter': 18, 'group_order': 2420, 'label': '11D5', 'order': 11, 'powers': [28, 30, 1], 'representative': 1190, 'size': 10}
  • id: 109385608
    {'aut_label': '22A', 'centralizer': '10.a1.a1', 'counter': 33, 'group_counter': 18, 'group_order': 2420, 'label': '22A', 'order': 22, 'powers': [21, 33, 2], 'representative': 110, 'size': 10}
  • id: 109385609
    {'aut_label': '22A', 'centralizer': '10.a1.a1', 'counter': 34, 'group_counter': 18, 'group_order': 2420, 'label': '22B', 'order': 22, 'powers': [22, 34, 2], 'representative': 1220, 'size': 10}
  • id: 109385610
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 35, 'group_counter': 18, 'group_order': 2420, 'label': '22C1', 'order': 22, 'powers': [23, 37, 2], 'representative': 120, 'size': 10}
  • id: 109385611
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 36, 'group_counter': 18, 'group_order': 2420, 'label': '22C3', 'order': 22, 'powers': [25, 38, 2], 'representative': 200, 'size': 10}
  • id: 109385612
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 37, 'group_counter': 18, 'group_order': 2420, 'label': '22C5', 'order': 22, 'powers': [27, 36, 2], 'representative': 140, 'size': 10}
  • id: 109385613
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 38, 'group_counter': 18, 'group_order': 2420, 'label': '22C7', 'order': 22, 'powers': [26, 39, 2], 'representative': 160, 'size': 10}
  • id: 109385614
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 39, 'group_counter': 18, 'group_order': 2420, 'label': '22C9', 'order': 22, 'powers': [24, 35, 2], 'representative': 150, 'size': 10}
  • id: 109385616
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 40, 'group_counter': 18, 'group_order': 2420, 'label': '22D1', 'order': 22, 'powers': [28, 42, 2], 'representative': 130, 'size': 10}
  • id: 109385617
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 41, 'group_counter': 18, 'group_order': 2420, 'label': '22D3', 'order': 22, 'powers': [30, 43, 2], 'representative': 180, 'size': 10}
  • id: 109385618
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 42, 'group_counter': 18, 'group_order': 2420, 'label': '22D5', 'order': 22, 'powers': [32, 41, 2], 'representative': 170, 'size': 10}
  • id: 109385619
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 43, 'group_counter': 18, 'group_order': 2420, 'label': '22D7', 'order': 22, 'powers': [31, 44, 2], 'representative': 210, 'size': 10}
  • id: 109385620
    {'aut_label': '22C1', 'centralizer': '10.a1.a1', 'counter': 44, 'group_counter': 18, 'group_order': 2420, 'label': '22D9', 'order': 22, 'powers': [29, 40, 2], 'representative': 190, 'size': 10}
• 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: 4250719
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4250727
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4250728
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4250729
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4250730
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1e', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
  • id: 4250731
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1f', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4], 'schur_index': 1}
  • id: 4250732
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1g', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4], 'schur_index': 1}
  • id: 4250733
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.1h', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
  • id: 4250734
    {'cdim': 10, 'counter': 9, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10a', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4250720
    {'cdim': 10, 'counter': 10, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10b', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4250721
    {'cdim': 10, 'counter': 11, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10c', 'multiplicity': 1, 'nt': [22, 6], 'qdim': 10, 'qvalues': [10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -10, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4250722
    {'cdim': 10, 'counter': 12, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10d', 'multiplicity': 1, 'nt': [22, 6], 'qdim': 10, 'qvalues': [10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -10, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4250723
    {'cdim': 10, 'counter': 13, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10e', 'multiplicity': 5, 'nt': [55, 0], 'qdim': 50, 'qvalues': [50, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 6, -5, -5, -5, 6, -5, 6, -5, 6, -5, 6, -5, 6, -5, 6, 6, -5, -5, 6, -5, -5, 6, -5], 'schur_index': 1}
  • id: 4250724
    {'cdim': 10, 'counter': 14, 'faithful': False, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10f', 'multiplicity': 5, 'nt': [55, 0], 'qdim': 50, 'qvalues': [50, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -5, -5, 6, -5, -5, 6, -5, 6, -5, 6, -5, 6, -5, -5, -5, -5, 6, -5, -5, 6, 6, -5, 6], 'schur_index': 1}
  • id: 4250725
    {'cdim': 10, 'counter': 15, 'faithful': True, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10g', 'multiplicity': 5, 'nt': [110, 0], 'qdim': 50, 'qvalues': [50, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 6, -5, -5, -5, 6, -5, 6, -5, 6, -5, 6, 5, -6, 5, -6, -6, 5, 5, -6, 5, 5, -6, 5], 'schur_index': 1}
  • id: 4250726
    {'cdim': 10, 'counter': 16, 'faithful': True, 'group': '2420.r', 'group_order': 2420, 'image': None, 'label': '2420.r.10h', 'multiplicity': 5, 'nt': [110, 0], 'qdim': 50, 'qvalues': [50, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -5, -5, 6, -5, -5, 6, -5, 6, -5, 6, -5, -6, 5, 5, 5, 5, -6, 5, 5, -6, -6, 5, -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: 6293279
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 2420, 'label': '2420.r.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293290
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 1210, 'label': '2420.r.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293301
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 1210, 'label': '2420.r.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293312
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 1210, 'label': '2420.r.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293318
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 484, 'label': '2420.r.1e1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293319
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 484, 'label': '2420.r.1e2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293320
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 484, 'label': '2420.r.1e3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[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: 6293321
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 484, 'label': '2420.r.1e4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[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: 6293322
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 242, 'label': '2420.r.1f1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -1]], [[1, -2]], [[-1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-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, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293280
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 242, 'label': '2420.r.1f2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 1]], [[1, 2]], [[-1, -2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-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, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293281
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 242, 'label': '2420.r.1f3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, 2]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[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: 6293282
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 242, 'label': '2420.r.1f4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, -2]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[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: 6293283
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 242, 'label': '2420.r.1g1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[1, -1]], [[-1, -2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[1, 1]], [[1, -2]], [[-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, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293284
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 242, 'label': '2420.r.1g2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[1, 1]], [[-1, 2]], [[1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[1, -1]], [[1, 2]], [[-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, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293285
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 242, 'label': '2420.r.1g3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[1, 2]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[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: 6293286
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 242, 'label': '2420.r.1g4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[1, -2]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[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: 6293287
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 242, 'label': '2420.r.1h1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[1, -2]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293288
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 242, 'label': '2420.r.1h2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[1, 2]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293289
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 242, 'label': '2420.r.1h3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[1, -1]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[1, -2]], [[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: 6293291
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 2420, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 242, 'label': '2420.r.1h4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[1, 1]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[1, 2]], [[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: 6293292
    {'center': '110.a1.b1', 'center_index': 110, 'center_order': 22, 'counter': 21, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.b1', 'kernel_order': 22, 'label': '2420.r.10a', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 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]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293293
    {'center': '110.a1.a1', 'center_index': 110, 'center_order': 22, 'counter': 22, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.a1', 'kernel_order': 22, 'label': '2420.r.10b', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 6293294
    {'center': '110.a1.b1', 'center_index': 110, 'center_order': 22, 'counter': 23, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '220.7', 'image_order': 220, 'indicator': 1, 'kernel': '220.a1.b1', 'kernel_order': 11, 'label': '2420.r.10c', 'nt': [22, 6], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[10, 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]], [[-10, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293295
    {'center': '110.a1.a1', 'center_index': 110, 'center_order': 22, 'counter': 24, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '220.7', 'image_order': 220, 'indicator': 1, 'kernel': '220.a1.a1', 'kernel_order': 11, 'label': '2420.r.10d', 'nt': [22, 6], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[10, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-10, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 6293296
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 25, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10e1', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]]]}
  • id: 6293297
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 26, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10e2', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]]]}
  • id: 6293298
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 27, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10e3', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]]]}
  • id: 6293299
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10e4', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]]]}
  • id: 6293300
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10e5', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]]]}
  • id: 6293302
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 30, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10f1', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]]]}
  • id: 6293303
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10f2', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]]]}
  • id: 6293304
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10f3', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]]]}
  • id: 6293305
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 33, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10f4', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]]]}
  • id: 6293306
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 34, 'cyclotomic_n': 11, 'dim': 10, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '1210.10', 'image_order': 1210, 'indicator': 1, 'kernel': '1210.a1.a1', 'kernel_order': 2, 'label': '2420.r.10f5', 'nt': [55, 0], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]]]}
  • id: 6293307
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10g1', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[1, 0]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[1, 0]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]]]}
  • id: 6293308
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 36, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10g2', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[1, 0]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[1, 0]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]]]}
  • id: 6293309
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 37, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10g3', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[1, 0]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[1, 0]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]]]}
  • id: 6293310
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 38, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10g4', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[1, 0]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[1, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]]]}
  • id: 6293311
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10g5', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[1, 0]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[1, 0]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]]]}
  • id: 6293313
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10h1', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-1, 0]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[1, 0]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[1, 0]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]]]}
  • id: 6293314
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10h2', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[1, 0]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[1, 0]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]]]}
  • id: 6293315
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10h3', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-1, 0]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[1, 0]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[1, 0]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]]]}
  • id: 6293316
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 43, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10h4', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[-1, 0]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-1, 0]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[1, 0]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[1, 0]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]]]}
  • id: 6293317
    {'center': '1210.a1.a1', 'center_index': 1210, 'center_order': 2, 'counter': 44, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [-1, 3, 3, -4, -1, 1], 'group': '2420.r', 'group_counter': 18, 'group_order': 2420, 'image': None, 'image_isoclass': '2420.r', 'image_order': 2420, 'indicator': 1, 'kernel': '2420.a1.a1', 'kernel_order': 1, 'label': '2420.r.10h5', 'nt': [110, 0], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [2, 1], [2, 3], [2, -3], [2, -1]], [[-1, 0], [1, 2], [-1, 3], [1, 4], [-1, 5], [-1, -5], [1, -4], [-1, -3], [1, -2]], [[-1, 0]], [[2, 0], [2, 4], [2, 5], [2, -5], [2, -4]], [[-1, 0]], [[1, 2], [2, 3], [2, 4], [2, -4], [2, -3], [1, -2]], [[2, 0], [2, 2], [2, 3], [2, -3], [2, -2]], [[2, 3], [1, 4], [2, 5], [2, -5], [1, -4], [2, -3]], [[2, 0], [2, 1], [2, 4], [2, -4], [2, -1]], [[-2, 0], [-2, 2], [-1, 3], [-2, 4], [-2, -4], [-1, -3], [-2, -2]], [[2, 0], [2, 2], [2, 5], [2, -5], [2, -2]], [[-2, 0], [-2, 3], [-2, 4], [-1, 5], [-1, -5], [-2, -4], [-2, -3]], [[-2, 0], [-2, 2], [-2, 5], [-2, -5], [-2, -2]], [[-2, 3], [-1, 4], [-2, 5], [-2, -5], [-1, -4], [-2, -3]], [[1, 0]], [[2, 0], [2, 3], [2, 4], [1, 5], [1, -5], [2, -4], [2, -3]], [[1, 0], [-1, 2], [1, 3], [-1, 4], [1, 5], [1, -5], [-1, -4], [1, -3], [-1, -2]], [[-2, 0], [-2, 4], [-2, 5], [-2, -5], [-2, -4]], [[1, 0]], [[2, 0], [2, 2], [1, 3], [2, 4], [2, -4], [1, -3], [2, -2]], [[-2, 0], [-2, 1], [-2, 4], [-2, -4], [-2, -1]], [[-2, 0], [-2, 2], [-2, 3], [-2, -3], [-2, -2]], [[-1, 2], [-2, 3], [-2, 4], [-2, -4], [-2, -3], [-1, -2]], [[-2, 0], [-2, 1], [-2, 3], [-2, -3], [-2, -1]]]}
• 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: 64346561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 2420, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 110, 'label': '2420.r.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2420.r', 'subgroup_hash': 2157492669750725759, 'subgroup_order': 2420, 'subgroup_tex': 'C_{22}:F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1210, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2420.r.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.20', 'subgroup_hash': 20, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}^2:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1210, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2420.r.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.10', 'subgroup_hash': 10, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346594
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1210, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '2420.r.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.10', 'subgroup_hash': 10, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 605, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 55, 'label': '2420.r.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.6', 'subgroup_hash': 6, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 64346607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 484, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 22, 'label': '2420.r.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '484.11', 'subgroup_hash': 11, 'subgroup_order': 484, 'subgroup_tex': 'C_{11}:D_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 64346608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': True, 'core_order': 242, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2420.r.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.5', 'subgroup_hash': 5, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}\\times C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 64346609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 242, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2420.r.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 242, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2420.r.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346562
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 22, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.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': 11, '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': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346563
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 22, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.11.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.b1', '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': 11, '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': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346564
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': True, 'core_order': 121, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 11, 'label': '2420.r.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 11}
  • id: 64346565
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 22, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, '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': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346566
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 22, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.22.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.a1.b1', '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': 22, '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': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346567
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.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': 22, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346568
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.22.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.b1.b1', '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': 22, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346569
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.22.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.b1.c1', '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': 22, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346570
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.22.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.b1.d1', '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': 22, '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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346571
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.44.a1.a1', 'maximal': False, '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': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 64346573
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.44.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.a1.b1', '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': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
  • id: 64346574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 22, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, '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: 64346575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 22, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.55.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.a1.b1', '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': 55, '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: 64346576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.55.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.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': 55, '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: 64346577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.55.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.b1.b1', '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': 55, '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: 64346578
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 22, 'counter': 25, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2420.r.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 64346579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 22, 'counter': 26, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2420.r.110.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
  • id: 64346580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.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': 110, '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: 64346581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.110.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.b1.b1', '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': 110, '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: 64346582
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, '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: 64346584
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.c1.b1', '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': 110, '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: 64346585
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.c1.c1', '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': 110, '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: 64346586
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.c1.d1', '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': 110, '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: 64346587
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, '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: 64346588
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.d1.b1', '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': 110, '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: 64346589
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.d1.c1', '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': 110, '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: 64346590
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2420.r.110.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.d1.d1', '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': 110, '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: 64346591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '2420.r.121.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '121.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': 121, '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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 11, 'counter': 38, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2420.r.220.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '220.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '220.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 220, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_{11}', 'simple': True, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 11, 'counter': 39, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '2420.r.220.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '220.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '220.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 220, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
  • id: 64346595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.220.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.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': 220, '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': 0}
  • id: 64346596
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 242, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.220.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.b1.b1', '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': 220, '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': 0}
  • id: 64346597
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.242.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346598
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.242.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346599
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.242.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.b1.b1', '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': 242, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 64346600
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '2420.r.484.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '484.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': 484, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
  • id: 64346601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '2420.r.605.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.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': 605, '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: 64346602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': True, 'central_factor': False, 'centralizer_order': 2420, 'characteristic': True, 'core_order': 2, 'counter': 47, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '2420.r.1210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1210.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1210.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1210, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}:F_{11}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 64346603
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.1210.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.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': 1210, '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: 64346604
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '2420.r.1210.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.b1.b1', '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': 1210, '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: 64346606
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '2420.r', 'ambient_counter': 18, 'ambient_order': 2420, 'ambient_tex': 'C_{22}:F_{11}', 'central': True, 'central_factor': False, 'centralizer_order': 2420, 'characteristic': True, 'core_order': 1, 'counter': 50, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '2420.r.2420.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2420.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '2420.r', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2157492669750725759, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2420, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{22}:F_{11}', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D2', 'C5'], '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: 64346561
    {'ambient': '2420.r', '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': '1210.a1.a1', 'complements': ['2420.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '5.a1.a1', '11.a1.a1', '11.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6353, 5857, 4863, 2963, 4741, 4538, 3669, 4475], 'generators': [5, 2, 10, 1210, 220], 'label': '2420.r.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1210.10', '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': '1210.10'}
  • id: 64346562
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '220.7', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.b1.c1', '55.a1.a1', '121.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5834, -1, 4037, -1, 7373, -1, 3256, -1], 'generators': [5, 2, 220, 1210], 'label': '2420.r.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346563
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '220.7', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.b1', '22.b1.b1', '22.b1.d1', '55.a1.b1', '121.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [5834, -1, 8183, -1, 7373, -1, 4082, -1], 'generators': [5, 2, 10, 1210], 'label': '2420.r.11.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '11.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346564
    {'ambient': '2420.r', 'aut_centralizer_order': 242, 'aut_label': '20.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '200.31', 'aut_weyl_index': 242, 'centralizer': '10.a1.a1', 'complements': ['121.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['220.a1.a1', '220.a1.b1', '220.b1.a1', '220.b1.b1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4065, 3514, 2425, 5766, 2913, 5137, 6627, 6284], 'generators': [10, 220], 'label': '2420.r.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'normal_contains': ['220.a1.a1', '220.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '2420.r', 'quotient_action_image': '10.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 64346565
    {'ambient': '2420.r', 'aut_centralizer_order': 20, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '110.a1.a1', '242.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8565, -1, 2464, -1, 7678, -1, 2053, -1], 'generators': [1210, 220, 2], 'label': '2420.r.22.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346566
    {'ambient': '2420.r', 'aut_centralizer_order': 20, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.b1'], 'contains': ['44.a1.b1', '110.a1.b1', '242.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [8565, -1, 7642, -1, 7678, -1, 3042, -1], 'generators': [1210, 10, 2], 'label': '2420.r.22.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '22.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346567
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '110.c1.a1', '242.b1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6303, -1, 1158, -1, 6376, -1, 176, -1], 'generators': [5, 220, 2], 'label': '2420.r.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346568
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.b1'], 'contains': ['44.a1.b1', '110.c1.b1', '242.b1.a1'], 'core': '220.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [6303, -1, 6219, -1, 6376, -1, 620, -1], 'generators': [5, 10, 2], 'label': '2420.r.22.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '22.b1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346569
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '11.a1.a1'], 'contains': ['44.a1.a1', '110.c1.c1', '242.b1.b1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6303, -1, 4523, -1, 6376, -1, 4592, -1], 'generators': [115, 220, 2], 'label': '2420.r.22.b1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.c1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346570
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '11.a1.b1'], 'contains': ['44.a1.b1', '110.c1.d1', '242.b1.b1'], 'core': '220.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [6303, -1, 8853, -1, 6376, -1, 5036, -1], 'generators': [1215, 10, 2], 'label': '2420.r.22.b1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '22.b1.d1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346571
    {'ambient': '2420.r', 'aut_centralizer_order': 20, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.a1', '22.b1.a1', '22.b1.c1'], 'contains': ['220.a1.a1', '484.a1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9513, -1, 1598, -1, 6376, -1, 1818, -1], 'generators': [2, 220], 'label': '2420.r.44.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '2420.r', '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': '110.1'}
  • id: 64346572
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 2, 'centralizer': '1210.a1.a1', 'complements': ['1210.b1.a1', '1210.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.a1.a1', '22.a1.a1', '22.a1.b1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9412, 8612, 4053, 8084, 5628, 4538, 2292, 5752], 'generators': [1210, 10, 220, 2], 'label': '2420.r.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', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
  • id: 64346573
    {'ambient': '2420.r', 'aut_centralizer_order': 20, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.b1', '22.b1.b1', '22.b1.d1'], 'contains': ['220.a1.b1', '484.a1.a1'], 'core': '220.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [9513, -1, 7418, -1, 6376, -1, 2425, -1], 'generators': [2, 10], 'label': '2420.r.44.a1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '44.a1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346574
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '220.7', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '110.c1.a1', '110.c1.c1', '605.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5784, -1, 3033, -1, 4261, -1, 5485, -1], 'generators': [5, 220, 1210], 'label': '2420.r.55.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346575
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '220.7', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.b1'], 'contains': ['110.a1.b1', '110.c1.b1', '110.c1.d1', '605.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [5784, -1, 9489, -1, 4261, -1, 5938, -1], 'generators': [5, 10, 1210], 'label': '2420.r.55.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '55.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346576
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '220.7', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['110.b1.a1', '110.d1.a1', '110.d1.c1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [1258, -1, 3748, -1, 328, -1, 8855, -1], 'generators': [5, 450, 1210], 'label': '2420.r.55.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '55.b1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 64346577
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': 110, 'aut_weyl_group': '220.7', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['110.b1.b1', '110.d1.b1', '110.d1.d1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [1258, -1, 6715, -1, 328, -1, 9309, -1], 'generators': [5, 230, 1210], 'label': '2420.r.55.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.b1', 'old_label': '55.b1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.b1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 64346578
    {'ambient': '2420.r', 'aut_centralizer_order': 2420, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': ['22.b1.b1', '22.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'contains': ['220.a1.a1', '1210.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8350, 5293, 2112, 6252, 5415, 7120, 4765, 8770], 'generators': [1210, 220], 'label': '2420.r.110.a1.a1', 'mobius_quo': 1, 'mobius_sub': -11, 'normal_closure': '110.a1.a1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['220.a1.a1', '1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 64346579
    {'ambient': '2420.r', 'aut_centralizer_order': 2420, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': ['22.b1.a1', '22.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.b1', '55.a1.b1'], 'contains': ['220.a1.b1', '1210.a1.a1'], 'core': '110.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8350, 5293, 8847, 8607, 5415, 7120, 5214, 7600], 'generators': [1210, 10], 'label': '2420.r.110.a1.b1', 'mobius_quo': 1, 'mobius_sub': -11, 'normal_closure': '110.a1.b1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['220.a1.b1', '1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.b1', 'projective_image': '1210.10', 'quotient_action_image': '10.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '110.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 64346580
    {'ambient': '2420.r', 'aut_centralizer_order': 484, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '55.b1.a1'], 'contains': ['220.b1.a1', '1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2231, -1, 2815, -1, 1999, -1, 8463, -1], 'generators': [1210, 450], 'label': '2420.r.110.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '110.b1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64346581
    {'ambient': '2420.r', 'aut_centralizer_order': 484, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '55.b1.b1'], 'contains': ['220.b1.b1', '1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2231, -1, 5867, -1, 1999, -1, 8911, -1], 'generators': [1210, 230], 'label': '2420.r.110.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '110.b1.b1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64346582
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '22.b1.a1', '55.a1.a1'], 'contains': ['220.a1.a1', '1210.b1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5784, -1, 198, -1, 4594, -1, 3858, -1], 'generators': [5, 220], 'label': '2420.r.110.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '110.c1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346583
    {'ambient': '2420.r', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 2, 'centralizer': '1210.a1.a1', 'complements': ['1210.a1.a1', '1210.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.b1.a1', '22.b1.a1', '22.b1.b1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6998, 3428, 2989, 4514, 3864, 1273, 1201, 991], 'generators': [5, 10, 220, 2], 'label': '2420.r.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '2420.r', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
  • id: 64346584
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '22.b1.b1', '55.a1.b1'], 'contains': ['220.a1.b1', '1210.b1.a1'], 'core': '220.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [5784, -1, 6576, -1, 4594, -1, 4312, -1], 'generators': [5, 10], 'label': '2420.r.110.c1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '110.c1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346585
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '22.b1.c1', '55.a1.a1'], 'contains': ['220.a1.a1', '1210.b1.b1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5784, -1, 3948, -1, 4594, -1, 5668, -1], 'generators': [115, 220], 'label': '2420.r.110.c1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '110.c1.c1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346586
    {'ambient': '2420.r', 'aut_centralizer_order': 10, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '22.b1.d1', '55.a1.b1'], 'contains': ['220.a1.b1', '1210.b1.b1'], 'core': '220.a1.b1', 'coset_action_label': None, 'count': 11, 'diagramx': [5784, -1, 9802, -1, 4594, -1, 6122, -1], 'generators': [115, 10], 'label': '2420.r.110.c1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.b1', 'old_label': '110.c1.d1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
  • id: 64346587
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 220, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '55.b1.a1'], 'contains': ['220.b1.a1', '1210.b1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [449, -1, 1192, -1, 1177, -1, 7555, -1], 'generators': [5, 450], 'label': '2420.r.110.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.d1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 64346588
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 220, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '55.b1.b1'], 'contains': ['220.b1.b1', '1210.b1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [449, -1, 5158, -1, 1177, -1, 8009, -1], 'generators': [5, 230], 'label': '2420.r.110.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.b1', 'old_label': '110.d1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.b1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 64346589
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 220, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '55.b1.a1'], 'contains': ['220.b1.a1', '1210.b1.b1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [449, -1, 4445, -1, 1177, -1, 9365, -1], 'generators': [115, 450], 'label': '2420.r.110.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.a1', 'old_label': '110.d1.c1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.c1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 64346590
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': 220, 'aut_weyl_group': '110.1', 'aut_weyl_index': 440, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '55.b1.b1'], 'contains': ['220.b1.b1', '1210.b1.b1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 55, 'diagramx': [449, -1, 7290, -1, 1177, -1, 9819, -1], 'generators': [115, 230], 'label': '2420.r.110.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '55.b1.b1', 'old_label': '110.d1.d1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.d1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
  • id: 64346591
    {'ambient': '2420.r', 'aut_centralizer_order': 100, 'aut_label': '121.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '4.2', 'aut_weyl_index': 12100, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '11.a1.b1'], 'contains': ['242.a1.a1', '242.b1.a1', '242.b1.b1', '605.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5418, -1, 6208, -1, 9331, -1, 3955, -1], 'generators': [5, 2, 1210], 'label': '2420.r.121.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '121.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346592
    {'ambient': '2420.r', 'aut_centralizer_order': 2420, 'aut_label': '220.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': ['11.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '44.a1.a1', '110.a1.a1', '110.c1.a1', '110.c1.c1'], 'contains': ['2420.a1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9551, 3926, 628, 5075, 5305, 5752, 4765, 7573], 'generators': [220], 'label': '2420.r.220.a1.a1', 'mobius_quo': -1, 'mobius_sub': 22, 'normal_closure': '220.a1.a1', 'normal_contained_in': ['20.a1.a1', '110.a1.a1'], 'normal_contains': ['2420.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '220.a1.a1', 'projective_image': '2420.r', 'quotient_action_image': '10.2', 'quotient_action_kernel': '22.2', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '220.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 64346593
    {'ambient': '2420.r', 'aut_centralizer_order': 2420, 'aut_label': '220.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '44.a1.b1', '110.a1.b1', '110.c1.b1', '110.c1.d1'], 'contains': ['2420.a1.a1'], 'core': '220.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9551, 3926, 8897, 7429, 5305, 5752, 5214, 6403], 'generators': [10], 'label': '2420.r.220.a1.b1', 'mobius_quo': -1, 'mobius_sub': 22, 'normal_closure': '220.a1.b1', 'normal_contained_in': ['20.a1.a1', '110.a1.b1'], 'normal_contains': ['2420.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '220.a1.b1', 'projective_image': '2420.r', 'quotient_action_image': '10.2', 'quotient_action_kernel': '22.2', 'quotient_action_kernel_order': 22, 'quotient_fusion': None, 'short_label': '220.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 64346594
    {'ambient': '2420.r', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 2, 'centralizer': '1210.a1.a1', 'complements': ['1210.a1.a1', '1210.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.b1.b1', '22.b1.c1', '22.b1.d1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6998, 3428, 6192, 1393, 3864, 1273, 4924, 3212], 'generators': [115, 10, 220, 2], 'label': '2420.r.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '2420.r', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
  • id: 64346595
    {'ambient': '2420.r', 'aut_centralizer_order': 484, 'aut_label': '220.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '110.b1.a1', '110.d1.a1', '110.d1.c1'], 'contains': ['2420.a1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2219, -1, 1158, -1, 2461, -1, 7555, -1], 'generators': [450], 'label': '2420.r.220.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '220.b1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64346596
    {'ambient': '2420.r', 'aut_centralizer_order': 484, 'aut_label': '220.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4840, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '110.b1.b1', '110.d1.b1', '110.d1.d1'], 'contains': ['2420.a1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2219, -1, 4300, -1, 2461, -1, 8009, -1], 'generators': [230], 'label': '2420.r.220.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '220.b1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 64346597
    {'ambient': '2420.r', 'aut_centralizer_order': 200, 'aut_label': '242.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '22.a1.b1', '121.a1.a1'], 'contains': ['484.a1.a1', '1210.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [7340, -1, 4723, -1, 8149, -1, 2955, -1], 'generators': [1210, 2], 'label': '2420.r.242.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346598
    {'ambient': '2420.r', 'aut_centralizer_order': 100, 'aut_label': '242.b1', 'aut_quo_index': None, 'aut_stab_index': 242, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.b1.a1', '22.b1.b1', '121.a1.a1'], 'contains': ['484.a1.a1', '1210.b1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6100, -1, 3597, -1, 7336, -1, 1288, -1], 'generators': [5, 2], 'label': '2420.r.242.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.b1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346599
    {'ambient': '2420.r', 'aut_centralizer_order': 100, 'aut_label': '242.b1', 'aut_quo_index': None, 'aut_stab_index': 242, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.b1.c1', '22.b1.d1', '121.a1.a1'], 'contains': ['484.a1.a1', '1210.b1.b1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6100, -1, 6632, -1, 7336, -1, 3404, -1], 'generators': [1215, 2], 'label': '2420.r.242.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.b1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346600
    {'ambient': '2420.r', 'aut_centralizer_order': 200, 'aut_label': '484.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1.a1', '44.a1.b1', '242.a1.a1', '242.b1.a1', '242.b1.b1'], 'contains': ['2420.a1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [7629, -1, 4372, -1, 6855, -1, 2690, -1], 'generators': [2], 'label': '2420.r.484.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '484.a1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '484.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346601
    {'ambient': '2420.r', 'aut_centralizer_order': 200, 'aut_label': '605.a1', 'aut_quo_index': None, 'aut_stab_index': 121, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24200, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '55.a1.b1', '55.b1.a1', '55.b1.b1', '121.a1.a1'], 'contains': ['1210.a1.a1', '1210.b1.a1', '1210.b1.b1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4811, -1, 5917, -1, 3800, -1, 7116, -1], 'generators': [5, 1210], 'label': '2420.r.605.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346602
    {'ambient': '2420.r', 'aut_centralizer_order': 48400, 'aut_label': '1210.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 48400, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '110.a1.b1', '110.b1.a1', '110.b1.b1', '242.a1.a1', '605.a1.a1'], 'contains': ['2420.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6201, 5207, 4723, 6289, 4566, 7120, 5989, 8637], 'generators': [1210], 'label': '2420.r.1210.a1.a1', 'mobius_quo': -1, 'mobius_sub': 121, 'normal_closure': '1210.a1.a1', 'normal_contained_in': ['110.a1.a1', '110.a1.b1'], 'normal_contains': ['2420.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1210.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1210.10', 'quotient_action_kernel_order': 1210, 'quotient_fusion': None, 'short_label': '1210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346603
    {'ambient': '2420.r', 'aut_centralizer_order': 200, 'aut_label': '1210.b1', 'aut_quo_index': None, 'aut_stab_index': 242, 'aut_weyl_group': '1.1', 'aut_weyl_index': 48400, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '110.c1.b1', '110.d1.a1', '110.d1.b1', '242.b1.a1', '605.a1.a1'], 'contains': ['2420.a1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4811, -1, 3033, -1, 3901, -1, 5622, -1], 'generators': [5], 'label': '2420.r.1210.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.b1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346604
    {'ambient': '2420.r', 'aut_centralizer_order': 200, 'aut_label': '1210.b1', 'aut_quo_index': None, 'aut_stab_index': 242, 'aut_weyl_group': '1.1', 'aut_weyl_index': 48400, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.c1', '110.c1.d1', '110.d1.c1', '110.d1.d1', '242.b1.b1', '605.a1.a1'], 'contains': ['2420.a1.a1'], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4811, -1, 6983, -1, 3901, -1, 6356, -1], 'generators': [115], 'label': '2420.r.1210.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.b1.b1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346605
    {'ambient': '2420.r', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 2, 'centralizer': '1210.a1.a1', 'complements': ['605.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['20.a1.a1', '44.a1.a1', '44.a1.b1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8350, 3428, 3530, 6308, 5323, 2111, 1201, 2573], 'generators': [2, 220, 10], 'label': '2420.r.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '2420.r', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
  • id: 64346606
    {'ambient': '2420.r', 'aut_centralizer_order': None, 'aut_label': '2420.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': ['220.a1.a1', '220.a1.b1', '220.b1.a1', '220.b1.b1', '484.a1.a1', '1210.a1.a1', '1210.b1.a1', '1210.b1.b1'], 'contains': [], 'core': '2420.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6201, 4598, 4160, 6289, 4566, 6436, 5806, 7573], 'generators': [], 'label': '2420.r.2420.a1.a1', 'mobius_quo': 1, 'mobius_sub': -242, 'normal_closure': '2420.a1.a1', 'normal_contained_in': ['220.a1.a1', '220.a1.b1', '1210.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '2420.a1.a1', 'projective_image': '2420.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2420.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 64346607
    {'ambient': '2420.r', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48400.l', 'aut_weyl_index': 1, 'centralizer': '1210.a1.a1', 'complements': ['484.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '55.a1.a1', '55.a1.b1', '55.b1.a1', '55.b1.b1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2649, 6096, 4936, 2215, 2073, 8265, 6968, 8651], 'generators': [5, 10, 220, 1210], 'label': '2420.r.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
  • id: 64346608
    {'ambient': '2420.r', 'aut_centralizer_order': 242, 'aut_label': '10.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '200.31', 'aut_weyl_index': 242, 'centralizer': '10.a1.a1', 'complements': ['242.b1.a1', '242.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '110.a1.a1', '110.a1.b1', '110.b1.a1', '110.b1.b1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4090, 5988, 3959, 8084, 2969, 7427, 7397, 8651], 'generators': [1210, 220, 10], 'label': '2420.r.10.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '110.a1.a1', '110.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
  • id: 64346609
    {'ambient': '2420.r', 'aut_centralizer_order': 1, 'aut_label': '10.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 2, 'centralizer': '1210.a1.a1', 'complements': ['242.a1.a1', '242.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '110.c1.a1', '110.c1.b1', '110.d1.a1', '110.d1.b1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1006, 1388, 2414, 4233, 1417, 4556, 6540, 4475], 'generators': [5, 220, 10], 'label': '2420.r.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '2420.r', 'quotient_action_image': '5.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}
  • id: 64346610
    {'ambient': '2420.r', 'aut_centralizer_order': 1, 'aut_label': '10.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 2, 'centralizer': '1210.a1.a1', 'complements': ['242.a1.a1', '242.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '110.c1.c1', '110.c1.d1', '110.d1.c1', '110.d1.d1'], 'core': '10.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1006, 1388, 5956, 1505, 1417, 4556, 8253, 6417], 'generators': [115, 220, 10], 'label': '2420.r.10.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': ['2.b1.b1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '2420.r', 'quotient_action_image': '5.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1210.10'}