Abstract group data - 1728.2739

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [12, 12, 12, 6, 2, 12, 4], 'aut_gens': [[1, 8, 16, 192, 576], [1253, 1512, 216, 640, 1152], [1001, 296, 1116, 640, 576], [1101, 296, 1112, 640, 576], [1261, 904, 212, 1536, 1152], [1607, 40, 176, 1536, 576], [111, 1032, 220, 704, 576], [685, 808, 1052, 640, 576]], 'aut_group': None, 'aut_hash': 2629835471383323536, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 216, 'aut_perms': [5586604600515473327803401589697518993650169302549501980388178543700782407577433757989014222434587216891298390739554424512375570900219255968262973980019785332889375391410377579921931671256936902804587797569125250833062932359703458300308544544236393789248550908390685317129840438951804371682048240676011452975498901700570426649033095018193575282454997417044233182965008171446042547537766165195861274803764492484480, 4315586912238863791799191220908289359154458605483685829684787450943754954178063805726329841277230899873081659603693551942757496104204308180950754205123272869720535829017094466418090357009006265497684374826293187872035220841551634289305464121746978282995332702320370352628606850904021903389484256254318869930194104681415466633591058224807756885129549469543259492376867137298884992974364479765473552849331329241555, 9003747969058130694426692640383815438211506877117783266344050131018938031106978223351599745393126936409083813898680289186877689802221764837659997364559542711559692388719607256725623048361765934938223381548680088756297690208371754908489381799082382965049947305769941770966427129296476565270075163013409270804772667304971736077057627754560528726312118846383691002411584410608664836425254828672319425469458152564445, 307665811874148016447004299267354670947319129277325659904381471137865784977173848204976488400637448326473568465810211099064917579322567728520440504131862213426665926642227992553876107941504705705802456120034491475712263957459491468061330241729405886509255939037160856849576761969683982489476394630445313670799666220982356935457593835488713872864422287263268161330759580026806930589451827110079240743384983465869, 5563830021795489867077182481992658769099759570279103546943253579535446235152802154657218379798517179545655015025922807742204409183271362799487941830934959846161528837747153118012151549181781209416951089534542652554311440474170205813283088797743514278537450786305344670332433226966210752956097484693891021528040242655159859243448896274959712233242215247686794187839942768403732082737067341479929019579594092808806, 3605201672899053196904843541816909522873613315889553826718056064961396972477299590246805188927356365958304800497993232464780589090177143332238310180978220876722479995666609752290215116825947044445953238413217338543354912311494515833592703244137596030557673191586266021702860780681086913286071405137574785863367347512578771644369777233933546035561771117876166691763023123293205376072878159581567956521321575034698, 1381073729556781602415629882429642795824914245523456725011230933327263325790597357334476836662877385622698840330237957006439325785086128297545183314928567584611971262942790624635074539978848481625687555679167415812755200621571249498865382237498751402658589275574885597402952135046950414020446318034517779694257255040808781055378272414310477669376882387663143680387885321774502241804404858572173360757539409338505], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 18, 1, 2], [3, 2, 1, 1], [3, 12, 1, 2], [4, 2, 2, 1], [4, 18, 2, 1], [4, 36, 2, 2], [6, 2, 1, 3], [6, 12, 1, 6], [6, 36, 1, 2], [8, 36, 4, 2], [12, 4, 2, 1], [12, 12, 2, 2], [12, 18, 2, 2], [12, 24, 2, 1], [12, 72, 2, 2], [24, 36, 4, 2], [24, 36, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_3.C_2^6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.530', 'autcentquo_hash': 530, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times \\He_3:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 18, 2], [3, 2, 1], [3, 12, 2], [4, 2, 2], [4, 18, 2], [4, 36, 4], [6, 2, 3], [6, 12, 6], [6, 36, 2], [8, 36, 8], [12, 4, 2], [12, 12, 4], [12, 18, 4], [12, 24, 2], [12, 72, 4], [24, 36, 16]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '432.238', 'commutator_count': 1, 'commutator_label': '108.28', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 2739, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 18, 1, 2], [3, 2, 1, 1], [3, 12, 1, 2], [4, 2, 2, 1], [4, 18, 2, 1], [4, 36, 1, 2], [4, 36, 2, 1], [6, 2, 1, 3], [6, 12, 1, 6], [6, 36, 1, 2], [8, 36, 4, 2], [12, 4, 2, 1], [12, 12, 2, 2], [12, 18, 4, 1], [12, 24, 2, 1], [12, 72, 1, 2], [12, 72, 2, 1], [24, 36, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 24, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '24.9', 'frattini_quotient': '72.40', 'hash': 2739, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 2, 6, 3, 3], 'inner_gens': [[1, 104, 344, 64, 1152], [97, 8, 80, 384, 576], [841, 136, 16, 1536, 1152], [321, 392, 976, 192, 576], [1153, 8, 1168, 192, 576]], 'inner_hash': 238, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_6.\\SOPlus(4,2)', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4], [4, 26], [6, 16], [8, 2], [12, 4]], 'label': '1728.2739', 'linC_count': 80, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 14, 'linQ_dim': 14, 'linQ_dim_count': 6, 'linR_count': 48, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C6.S3^2:C8', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 37, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 68, 'number_divisions': 37, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 233, 'number_subgroup_classes': 259, 'number_subgroups': 2693, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 39], [3, 26], [4, 184], [6, 150], [8, 288], [12, 464], [24, 576]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 8, 80, 384, 576], [5, 8, 16, 192, 576], [1, 8, 20, 192, 576], [3, 104, 16, 192, 576]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 34, 'pgroup': 0, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 11], [6, 2], [8, 7], [12, 3], [16, 2], [24, 4]], 'representations': {'PC': {'code': 170168655471944561326511213571043981398672754331372323643338333180944475655, 'gens': [1, 4, 5, 8, 9], 'pres': [9, -2, -2, -2, -2, 2, -2, -3, 3, -3, 18, 46, 3747, 15484, 2533, 481, 130, 25925, 1112, 158, 12102, 1041, 4615, 3490, 6955, 3076, 925, 93320, 5876]}, 'Perm': {'d': 34, 'gens': [8718412404428147857424204088397687680, 51815897577805453130349842508196137, 59965767137463421604937366219840000, 355539313048, 18498, 4296764102400, 18479168858113004924989198066630656000, 27416555824158387127337166181343232000, 36378460562754640262695337877958656000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6.S_3^2:C_8', 'transitive_degree': 288, '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: 128380946
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2739, 'group_order': 1728, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 128380957
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 2739, 'group_order': 1728, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 96, 'size': 1}
  • id: 128380968
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 2739, 'group_order': 1728, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 100, 'size': 1}
  • id: 128380979
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 2739, 'group_order': 1728, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 4, 'size': 1}
  • id: 128380990
    {'aut_label': '2D', 'centralizer': '18.a1.a1', 'counter': 5, 'group_counter': 2739, 'group_order': 1728, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 8, 'size': 18}
  • id: 128381001
    {'aut_label': '2E', 'centralizer': '18.a1.a1', 'counter': 6, 'group_counter': 2739, 'group_order': 1728, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 12, 'size': 18}
  • id: 128381011
    {'aut_label': '3A', 'centralizer': '2.c1.a1', 'counter': 7, 'group_counter': 2739, 'group_order': 1728, 'label': '3A', 'order': 3, 'powers': [7, 1], 'representative': 1152, 'size': 2}
  • id: 128381012
    {'aut_label': '3B', 'centralizer': '12.e1.a1', 'counter': 8, 'group_counter': 2739, 'group_order': 1728, 'label': '3B', 'order': 3, 'powers': [8, 1], 'representative': 1600, 'size': 12}
  • id: 128381013
    {'aut_label': '3C', 'centralizer': '12.g1.a1', 'counter': 9, 'group_counter': 2739, 'group_order': 1728, 'label': '3C', 'order': 3, 'powers': [9, 1], 'representative': 64, 'size': 12}
  • id: 128380947
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 2739, 'group_order': 1728, 'label': '4A1', 'order': 4, 'powers': [4, 11], 'representative': 6, 'size': 2}
  • id: 128380948
    {'aut_label': '4A1', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 2739, 'group_order': 1728, 'label': '4A-1', 'order': 4, 'powers': [4, 10], 'representative': 2, 'size': 2}
  • id: 128380949
    {'aut_label': '4B1', 'centralizer': '18.c1.a1', 'counter': 12, 'group_counter': 2739, 'group_order': 1728, 'label': '4B1', 'order': 4, 'powers': [4, 13], 'representative': 1134, 'size': 18}
  • id: 128380950
    {'aut_label': '4B1', 'centralizer': '18.c1.a1', 'counter': 13, 'group_counter': 2739, 'group_order': 1728, 'label': '4B-1', 'order': 4, 'powers': [4, 12], 'representative': 1130, 'size': 18}
  • id: 128380951
    {'aut_label': '4C', 'centralizer': '36.f1.a1', 'counter': 14, 'group_counter': 2739, 'group_order': 1728, 'label': '4C', 'order': 4, 'powers': [2, 14], 'representative': 1588, 'size': 36}
  • id: 128380952
    {'aut_label': '4C', 'centralizer': '36.f1.a1', 'counter': 15, 'group_counter': 2739, 'group_order': 1728, 'label': '4D', 'order': 4, 'powers': [2, 15], 'representative': 1488, 'size': 36}
  • id: 128380953
    {'aut_label': '4E1', 'centralizer': '36.g1.a1', 'counter': 16, 'group_counter': 2739, 'group_order': 1728, 'label': '4E1', 'order': 4, 'powers': [4, 17], 'representative': 1106, 'size': 36}
  • id: 128380954
    {'aut_label': '4E1', 'centralizer': '36.g1.a1', 'counter': 17, 'group_counter': 2739, 'group_order': 1728, 'label': '4E-1', 'order': 4, 'powers': [4, 16], 'representative': 1110, 'size': 36}
  • id: 128380955
    {'aut_label': '6A', 'centralizer': '2.c1.a1', 'counter': 18, 'group_counter': 2739, 'group_order': 1728, 'label': '6A', 'order': 6, 'powers': [7, 2], 'representative': 672, 'size': 2}
  • id: 128380956
    {'aut_label': '6B', 'centralizer': '2.c1.a1', 'counter': 19, 'group_counter': 2739, 'group_order': 1728, 'label': '6B', 'order': 6, 'powers': [7, 3], 'representative': 676, 'size': 2}
  • id: 128380958
    {'aut_label': '6C', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 2739, 'group_order': 1728, 'label': '6C', 'order': 6, 'powers': [7, 4], 'representative': 1156, 'size': 2}
  • id: 128380959
    {'aut_label': '6D', 'centralizer': '12.e1.a1', 'counter': 21, 'group_counter': 2739, 'group_order': 1728, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 224, 'size': 12}
  • id: 128380960
    {'aut_label': '6E', 'centralizer': '12.g1.a1', 'counter': 22, 'group_counter': 2739, 'group_order': 1728, 'label': '6E', 'order': 6, 'powers': [9, 3], 'representative': 36, 'size': 12}
  • id: 128380961
    {'aut_label': '6F', 'centralizer': '12.e1.a1', 'counter': 23, 'group_counter': 2739, 'group_order': 1728, 'label': '6F', 'order': 6, 'powers': [8, 3], 'representative': 228, 'size': 12}
  • id: 128380962
    {'aut_label': '6G', 'centralizer': '12.e1.a1', 'counter': 24, 'group_counter': 2739, 'group_order': 1728, 'label': '6G', 'order': 6, 'powers': [8, 4], 'representative': 1476, 'size': 12}
  • id: 128380963
    {'aut_label': '6H', 'centralizer': '12.g1.a1', 'counter': 25, 'group_counter': 2739, 'group_order': 1728, 'label': '6H', 'order': 6, 'powers': [9, 4], 'representative': 388, 'size': 12}
  • id: 128380964
    {'aut_label': '6I', 'centralizer': '12.g1.a1', 'counter': 26, 'group_counter': 2739, 'group_order': 1728, 'label': '6I', 'order': 6, 'powers': [9, 2], 'representative': 608, 'size': 12}
  • id: 128380965
    {'aut_label': '6J', 'centralizer': '36.a1.a1', 'counter': 27, 'group_counter': 2739, 'group_order': 1728, 'label': '6J', 'order': 6, 'powers': [7, 5], 'representative': 584, 'size': 36}
  • id: 128380966
    {'aut_label': '6K', 'centralizer': '36.a1.a1', 'counter': 28, 'group_counter': 2739, 'group_order': 1728, 'label': '6K', 'order': 6, 'powers': [7, 6], 'representative': 588, 'size': 36}
  • id: 128380967
    {'aut_label': '8A1', 'centralizer': '36.l1.a1', 'counter': 29, 'group_counter': 2739, 'group_order': 1728, 'label': '8A1', 'order': 8, 'powers': [10, 31], 'representative': 1027, 'size': 36}
  • id: 128380969
    {'aut_label': '8A1', 'centralizer': '36.l1.a1', 'counter': 30, 'group_counter': 2739, 'group_order': 1728, 'label': '8A-1', 'order': 8, 'powers': [11, 32], 'representative': 1029, 'size': 36}
  • id: 128380970
    {'aut_label': '8A1', 'centralizer': '36.l1.a1', 'counter': 31, 'group_counter': 2739, 'group_order': 1728, 'label': '8A3', 'order': 8, 'powers': [11, 29], 'representative': 1025, 'size': 36}
  • id: 128380971
    {'aut_label': '8A1', 'centralizer': '36.l1.a1', 'counter': 32, 'group_counter': 2739, 'group_order': 1728, 'label': '8A-3', 'order': 8, 'powers': [10, 30], 'representative': 1031, 'size': 36}
  • id: 128380972
    {'aut_label': '8B1', 'centralizer': '36.k1.a1', 'counter': 33, 'group_counter': 2739, 'group_order': 1728, 'label': '8B1', 'order': 8, 'powers': [12, 35], 'representative': 1691, 'size': 36}
  • id: 128380973
    {'aut_label': '8B1', 'centralizer': '36.k1.a1', 'counter': 34, 'group_counter': 2739, 'group_order': 1728, 'label': '8B-1', 'order': 8, 'powers': [13, 36], 'representative': 597, 'size': 36}
  • id: 128380974
    {'aut_label': '8B1', 'centralizer': '36.k1.a1', 'counter': 35, 'group_counter': 2739, 'group_order': 1728, 'label': '8B3', 'order': 8, 'powers': [13, 33], 'representative': 593, 'size': 36}
  • id: 128380975
    {'aut_label': '8B1', 'centralizer': '36.k1.a1', 'counter': 36, 'group_counter': 2739, 'group_order': 1728, 'label': '8B-3', 'order': 8, 'powers': [12, 34], 'representative': 1695, 'size': 36}
  • id: 128380976
    {'aut_label': '12A1', 'centralizer': '4.a1.a1', 'counter': 37, 'group_counter': 2739, 'group_order': 1728, 'label': '12A1', 'order': 12, 'powers': [20, 10], 'representative': 578, 'size': 4}
  • id: 128380977
    {'aut_label': '12A1', 'centralizer': '4.a1.a1', 'counter': 38, 'group_counter': 2739, 'group_order': 1728, 'label': '12A-1', 'order': 12, 'powers': [20, 11], 'representative': 582, 'size': 4}
  • id: 128380978
    {'aut_label': '12B1', 'centralizer': '12.e1.a1', 'counter': 39, 'group_counter': 2739, 'group_order': 1728, 'label': '12B1', 'order': 12, 'powers': [24, 10], 'representative': 450, 'size': 12}
  • id: 128380980
    {'aut_label': '12B1', 'centralizer': '12.e1.a1', 'counter': 40, 'group_counter': 2739, 'group_order': 1728, 'label': '12B-1', 'order': 12, 'powers': [24, 11], 'representative': 454, 'size': 12}
  • id: 128380981
    {'aut_label': '12C1', 'centralizer': '12.e1.a1', 'counter': 41, 'group_counter': 2739, 'group_order': 1728, 'label': '12C1', 'order': 12, 'powers': [24, 10], 'representative': 258, 'size': 12}
  • id: 128380982
    {'aut_label': '12C1', 'centralizer': '12.e1.a1', 'counter': 42, 'group_counter': 2739, 'group_order': 1728, 'label': '12C-1', 'order': 12, 'powers': [24, 11], 'representative': 1094, 'size': 12}
  • id: 128380983
    {'aut_label': '12D1', 'centralizer': '18.c1.a1', 'counter': 43, 'group_counter': 2739, 'group_order': 1728, 'label': '12D1', 'order': 12, 'powers': [20, 12], 'representative': 1706, 'size': 18}
  • id: 128380984
    {'aut_label': '12D1', 'centralizer': '18.c1.a1', 'counter': 44, 'group_counter': 2739, 'group_order': 1728, 'label': '12D-1', 'order': 12, 'powers': [20, 13], 'representative': 558, 'size': 18}
  • id: 128380985
    {'aut_label': '12D5', 'centralizer': '18.c1.a1', 'counter': 45, 'group_counter': 2739, 'group_order': 1728, 'label': '12D5', 'order': 12, 'powers': [20, 12], 'representative': 554, 'size': 18}
  • id: 128380986
    {'aut_label': '12D5', 'centralizer': '18.c1.a1', 'counter': 46, 'group_counter': 2739, 'group_order': 1728, 'label': '12D-5', 'order': 12, 'powers': [20, 13], 'representative': 1710, 'size': 18}
  • id: 128380987
    {'aut_label': '12E1', 'centralizer': '24.e1.a1', 'counter': 47, 'group_counter': 2739, 'group_order': 1728, 'label': '12E1', 'order': 12, 'powers': [25, 10], 'representative': 194, 'size': 24}
  • id: 128380988
    {'aut_label': '12E1', 'centralizer': '24.e1.a1', 'counter': 48, 'group_counter': 2739, 'group_order': 1728, 'label': '12E-1', 'order': 12, 'powers': [25, 11], 'representative': 198, 'size': 24}
  • id: 128380989
    {'aut_label': '12F', 'centralizer': '72.l1.a1', 'counter': 49, 'group_counter': 2739, 'group_order': 1728, 'label': '12F', 'order': 12, 'powers': [26, 14], 'representative': 404, 'size': 72}
  • id: 128380991
    {'aut_label': '12F', 'centralizer': '72.l1.a1', 'counter': 50, 'group_counter': 2739, 'group_order': 1728, 'label': '12G', 'order': 12, 'powers': [26, 15], 'representative': 880, 'size': 72}
  • id: 128380992
    {'aut_label': '12H1', 'centralizer': '72.n1.a1', 'counter': 51, 'group_counter': 2739, 'group_order': 1728, 'label': '12H1', 'order': 12, 'powers': [25, 16], 'representative': 1558, 'size': 72}
  • id: 128380993
    {'aut_label': '12H1', 'centralizer': '72.n1.a1', 'counter': 52, 'group_counter': 2739, 'group_order': 1728, 'label': '12H-1', 'order': 12, 'powers': [25, 17], 'representative': 466, 'size': 72}
  • id: 128380994
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 53, 'group_counter': 2739, 'group_order': 1728, 'label': '24A1', 'order': 24, 'powers': [41, 29], 'representative': 193, 'size': 36}
  • id: 128380995
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 54, 'group_counter': 2739, 'group_order': 1728, 'label': '24A-1', 'order': 24, 'powers': [42, 30], 'representative': 391, 'size': 36}
  • id: 128380996
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 55, 'group_counter': 2739, 'group_order': 1728, 'label': '24A5', 'order': 24, 'powers': [41, 32], 'representative': 389, 'size': 36}
  • id: 128380997
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 56, 'group_counter': 2739, 'group_order': 1728, 'label': '24A-5', 'order': 24, 'powers': [42, 31], 'representative': 195, 'size': 36}
  • id: 128380998
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 57, 'group_counter': 2739, 'group_order': 1728, 'label': '24A7', 'order': 24, 'powers': [42, 30], 'representative': 199, 'size': 36}
  • id: 128380999
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 58, 'group_counter': 2739, 'group_order': 1728, 'label': '24A-7', 'order': 24, 'powers': [41, 29], 'representative': 385, 'size': 36}
  • id: 128381000
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 59, 'group_counter': 2739, 'group_order': 1728, 'label': '24A11', 'order': 24, 'powers': [42, 31], 'representative': 387, 'size': 36}
  • id: 128381002
    {'aut_label': '24A1', 'centralizer': '36.l1.a1', 'counter': 60, 'group_counter': 2739, 'group_order': 1728, 'label': '24A-11', 'order': 24, 'powers': [41, 32], 'representative': 197, 'size': 36}
  • id: 128381003
    {'aut_label': '24B1', 'centralizer': '36.k1.a1', 'counter': 61, 'group_counter': 2739, 'group_order': 1728, 'label': '24B1', 'order': 24, 'powers': [43, 33], 'representative': 17, 'size': 36}
  • id: 128381004
    {'aut_label': '24B1', 'centralizer': '36.k1.a1', 'counter': 62, 'group_counter': 2739, 'group_order': 1728, 'label': '24B-1', 'order': 24, 'powers': [44, 34], 'representative': 23, 'size': 36}
  • id: 128381005
    {'aut_label': '24B5', 'centralizer': '36.k1.a1', 'counter': 63, 'group_counter': 2739, 'group_order': 1728, 'label': '24B5', 'order': 24, 'powers': [45, 36], 'representative': 1173, 'size': 36}
  • id: 128381006
    {'aut_label': '24B5', 'centralizer': '36.k1.a1', 'counter': 64, 'group_counter': 2739, 'group_order': 1728, 'label': '24B-5', 'order': 24, 'powers': [46, 35], 'representative': 1171, 'size': 36}
  • id: 128381007
    {'aut_label': '24B5', 'centralizer': '36.k1.a1', 'counter': 65, 'group_counter': 2739, 'group_order': 1728, 'label': '24B7', 'order': 24, 'powers': [46, 34], 'representative': 1175, 'size': 36}
  • id: 128381008
    {'aut_label': '24B5', 'centralizer': '36.k1.a1', 'counter': 66, 'group_counter': 2739, 'group_order': 1728, 'label': '24B-7', 'order': 24, 'powers': [45, 33], 'representative': 1169, 'size': 36}
  • id: 128381009
    {'aut_label': '24B1', 'centralizer': '36.k1.a1', 'counter': 67, 'group_counter': 2739, 'group_order': 1728, 'label': '24B11', 'order': 24, 'powers': [44, 35], 'representative': 19, 'size': 36}
  • id: 128381010
    {'aut_label': '24B1', 'centralizer': '36.k1.a1', 'counter': 68, 'group_counter': 2739, 'group_order': 1728, 'label': '24B-11', 'order': 24, 'powers': [43, 36], 'representative': 21, 'size': 36}
• gps_qchar •

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

  
  
  • id: 9147100
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 9147111
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 9147122
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 9147131
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 9147132
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147133
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147136
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147101
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147134
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1g', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, -4, 4, 0, 4, -4, -4, 4, 4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147135
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.1h', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 4, -4, 0, 4, -4, -4, 4, 4, -4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147102
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.2c', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 4, 4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147103
    {'cdim': 4, 'counter': 12, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, -2, 1, 4, 4, 0, 0, 2, 2, 2, 2, 4, 4, 4, -2, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147104
    {'cdim': 4, 'counter': 13, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 1, -2, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 1, -2, -2, 1, -2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 4, 4, 1, 1, 1, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, 0, -1, -1, 0], 'schur_index': 1}
  • id: 9147105
    {'cdim': 4, 'counter': 14, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4c', 'multiplicity': 1, 'nt': [8, 19], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147106
    {'cdim': 4, 'counter': 15, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4d', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, -2, 1, 4, 4, 0, 0, -2, -2, -2, -2, 4, 4, 4, -2, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147107
    {'cdim': 4, 'counter': 16, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4e', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 1, -2, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 1, -2, -2, 1, -2, 1, 0, 0, -2, -2, 0, 0, 0, -2, 0, -2, 4, 4, 1, 1, 1, 1, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0], 'schur_index': 1}
  • id: 9147108
    {'cdim': 4, 'counter': 17, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4f', 'multiplicity': 1, 'nt': [12, 79], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, -2, 1, -4, -4, 0, 0, -2, 2, 2, -2, 4, 4, 4, -2, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147109
    {'cdim': 4, 'counter': 18, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4g', 'multiplicity': 1, 'nt': [12, 79], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, -2, 1, -4, -4, 0, 0, 2, -2, -2, 2, 4, 4, 4, -2, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147110
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4h', 'multiplicity': 1, 'nt': [16, 40], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9147119
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6a', 'multiplicity': 1, 'nt': [27, 76], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -3, 0, 0, 6, 6, -2, -2, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 2, 0, -3, -3, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1], 'schur_index': 1}
  • id: 9147120
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6b', 'multiplicity': 1, 'nt': [36, 277], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -3, 0, 0, 6, 6, -2, -2, 0, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, -2, -2, -2, 0, -2, 0, -3, -3, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1], 'schur_index': 1}
  • id: 9147112
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4i', 'multiplicity': 2, 'nt': [24, 213], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 8, 2, -4, -8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 2, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -2, -2, -2, -2, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147113
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4j', 'multiplicity': 2, 'nt': [24, 597], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 8, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, -2, 4, 4, 2, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147114
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4k', 'multiplicity': 2, 'nt': [24, 598], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 8, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, -2, 4, 4, 2, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, -6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147115
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4l', 'multiplicity': 2, 'nt': [24, 663], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 8, -4, 2, 0, 0, 0, 0, 0, -4, 4, 0, 8, -8, -8, -4, 2, -2, 4, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147116
    {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4m', 'multiplicity': 2, 'nt': [24, 663], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 8, -4, 2, 0, 0, 0, 0, 0, 4, -4, 0, 8, -8, -8, -4, 2, -2, 4, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147127
    {'cdim': 8, 'counter': 34, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.8a', 'multiplicity': 1, 'nt': [24, 596], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 8, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 4, -2, -2, -4, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147128
    {'cdim': 8, 'counter': 35, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.8b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 8, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 4, -2, 2, 4, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9147121
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6c', 'multiplicity': 2, 'nt': [18, 105], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 4, 4, -6, 0, 0, 12, 12, 4, 4, 0, 0, 0, 0, -6, -6, -6, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147123
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6d', 'multiplicity': 2, 'nt': [36, 672], 'qdim': 12, 'qvalues': [12, 12, 12, 12, -4, -4, -6, 0, 0, -12, -12, 4, 4, 0, 0, 0, 0, -6, -6, -6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147124
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6e', 'multiplicity': 2, 'nt': [36, 673], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 4, 4, -6, 0, 0, -12, -12, -4, -4, 0, 0, 0, 0, -6, -6, -6, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147117
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4n', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 16, 4, -8, 0, 0, 0, 0, 0, 0, 0, 0, -16, 16, -16, -4, 8, -8, -4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147118
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.4o', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 16, 4, -8, 0, 0, 0, 0, 0, 0, 0, 0, 16, -16, -16, 4, -8, 8, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147125
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6f', 'multiplicity': 4, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 24, -24, -24, -8, 8, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, 12, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147126
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.6g', 'multiplicity': 4, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, 24, -24, -24, 8, -8, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, 12, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147129
    {'cdim': 12, 'counter': 36, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.12a', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, -24, 24, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9147130
    {'cdim': 12, 'counter': 37, 'faithful': False, 'group': '1728.2739', 'group_order': 1728, 'image': None, 'label': '1728.2739.12b', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• 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: 21203869
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1728, 'label': '1728.2739.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 21203880
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 864, 'label': '1728.2739.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[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: 21203891
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 864, 'label': '1728.2739.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 21203902
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 864, 'label': '1728.2739.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 21203913
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 432, 'label': '1728.2739.1e1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
  • id: 21203924
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 432, 'label': '1728.2739.1e2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
  • id: 21203934
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 432, 'label': '1728.2739.1f1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 21203935
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 432, 'label': '1728.2739.1f2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 21203936
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 9, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 216, 'label': '1728.2739.1g1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-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, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]]]}
  • id: 21203870
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 10, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 216, 'label': '1728.2739.1g2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[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, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
  • id: 21203871
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 11, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 216, 'label': '1728.2739.1g3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-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, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]]]}
  • id: 21203872
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 12, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 216, 'label': '1728.2739.1g4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[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, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
  • id: 21203873
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 13, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 216, 'label': '1728.2739.1h1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[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, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]]]}
  • id: 21203874
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 14, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 216, 'label': '1728.2739.1h2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-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, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]]]}
  • id: 21203875
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 15, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 216, 'label': '1728.2739.1h3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[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, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]]]}
  • id: 21203876
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 16, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 216, 'label': '1728.2739.1h4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-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, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]]]}
  • id: 21203877
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 432, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.c1.a1', 'kernel_order': 216, 'label': '1728.2739.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203878
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 432, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 216, 'label': '1728.2739.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203879
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 432, 'counter': 19, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 108, 'label': '1728.2739.2c1', 'nt': [8, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203881
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 432, 'counter': 20, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 108, 'label': '1728.2739.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203882
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 21, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 24, 'label': '1728.2739.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203883
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 24, 'label': '1728.2739.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 21203884
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 108, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '32.6', 'image_order': 32, 'indicator': 1, 'kernel': '32.c1.a1', 'kernel_order': 54, 'label': '1728.2739.4c', 'nt': [8, 19], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203885
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 24, 'label': '1728.2739.4d', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203886
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 24, 'label': '1728.2739.4e', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 21203887
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 12, 'label': '1728.2739.4f', 'nt': [12, 79], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203888
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 12, 'label': '1728.2739.4g', 'nt': [12, 79], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203889
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 108, 'counter': 28, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '32.8', 'image_order': 32, 'indicator': -1, 'kernel': '32.b1.a1', 'kernel_order': 54, 'label': '1728.2739.4h', 'nt': [16, 40], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203890
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 29, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 12, 'label': '1728.2739.4i1', 'nt': [24, 213], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]]]}
  • id: 21203892
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 30, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '144.115', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 12, 'label': '1728.2739.4i2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]]]}
  • id: 21203893
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 31, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.386', 'image_order': 288, 'indicator': 0, 'kernel': '288.c1.a1', 'kernel_order': 6, 'label': '1728.2739.4j1', 'nt': [24, 597], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]]]}
  • id: 21203894
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 32, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.386', 'image_order': 288, 'indicator': 0, 'kernel': '288.c1.a1', 'kernel_order': 6, 'label': '1728.2739.4j2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]]]}
  • id: 21203895
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 33, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.386', 'image_order': 288, 'indicator': 1, 'kernel': '288.c1.a1', 'kernel_order': 6, 'label': '1728.2739.4k1', 'nt': [24, 598], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]]]}
  • id: 21203896
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 34, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.386', 'image_order': 288, 'indicator': 1, 'kernel': '288.c1.a1', 'kernel_order': 6, 'label': '1728.2739.4k2', 'nt': [24, 598], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]]]}
  • id: 21203897
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 35, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4l1', 'nt': [24, 663], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203898
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 36, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4l2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203899
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 37, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4m1', 'nt': [24, 663], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[2, 1]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203900
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 38, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4m2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203901
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 39, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.376', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.2739.4n1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6]], [[3, 6]], [[-3, 6]], [[3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 7]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 7]], [[1, 1], [1, 5]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 3], [-2, 7]], [[0, 0]], [[1, 3], [-2, 7]], [[-1, 1], [-1, 5]], [[0, 0]]]}
  • id: 21203903
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 40, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.376', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.2739.4n2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6]], [[-3, 6]], [[3, 6]], [[-3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-2, 7]], [[0, 0]], [[1, 3], [-2, 7]], [[-1, 3], [2, 7]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [2, 7]], [[0, 0]]]}
  • id: 21203904
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 41, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.376', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.2739.4n3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6]], [[3, 6]], [[-3, 6]], [[3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 7]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 3], [2, 7]], [[0, 0]], [[-1, 3], [2, 7]], [[1, 1], [1, 5]], [[0, 0]]]}
  • id: 21203905
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 42, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.376', 'image_order': 288, 'indicator': 0, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.2739.4n4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6]], [[-3, 6]], [[3, 6]], [[-3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[-1, 3], [2, 7]], [[0, 0]], [[-1, 3], [2, 7]], [[1, 3], [-2, 7]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[-1, 1], [-1, 5]], [[1, 3], [-2, 7]], [[0, 0]]]}
  • id: 21203906
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 43, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4o1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[0, 0]], [[2, 1]], [[4, 2]], [[-4, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 3]], [[0, 0]], [[-1, 3]], [[1, 3]], [[0, 0]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 3]], [[0, 0]]]}
  • id: 21203907
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 44, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4o2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 3]], [[-4, 2]], [[4, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[0, 0]], [[0, 0]], [[-1, 3]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[1, 3]], [[0, 0]], [[-1, 3]], [[1, 1]], [[0, 0]]]}
  • id: 21203908
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 45, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4o3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[0, 0]], [[-2, 1]], [[4, 2]], [[-4, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 3]], [[0, 0]], [[1, 3]], [[-1, 3]], [[0, 0]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 3]], [[0, 0]]]}
  • id: 21203909
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 46, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.374', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 6, 'label': '1728.2739.4o4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 3]], [[-4, 2]], [[4, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[0, 0]], [[0, 0]], [[1, 3]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[-1, 3]], [[0, 0]], [[1, 3]], [[-1, 1]], [[0, 0]]]}
  • id: 21203910
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 8, 'label': '1728.2739.6a', 'nt': [27, 76], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 21203911
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 48, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 8, 'label': '1728.2739.6b', 'nt': [36, 277], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 21203912
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 49, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 8, 'label': '1728.2739.6c1', 'nt': [18, 105], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]]]}
  • id: 21203914
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '216.87', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 8, 'label': '1728.2739.6c2', 'nt': [18, 105], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]]]}
  • id: 21203915
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '432.238', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 4, 'label': '1728.2739.6d1', 'nt': [36, 672], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]]]}
  • id: 21203916
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '432.238', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 4, 'label': '1728.2739.6d2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]]]}
  • id: 21203917
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '432.238', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 4, 'label': '1728.2739.6e1', 'nt': [36, 673], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]]]}
  • id: 21203918
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 54, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '432.238', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 4, 'label': '1728.2739.6e2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]]]}
  • id: 21203919
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 55, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6f1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 2]], [[6, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[0, 0]], [[2, 1]], [[0, 0]], [[-3, 2]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[0, 0]], [[1, 1]], [[1, 3]], [[0, 0]], [[0, 0]], [[-1, 3]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 3]]]}
  • id: 21203920
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 56, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6f2', 'nt': [72, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 2]], [[-6, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 3]], [[0, 0]], [[3, 2]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[0, 0]], [[-1, 3]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, 3]], [[0, 0]], [[1, 3]], [[0, 0]], [[0, 0]], [[-1, 1]]]}
  • id: 21203921
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 57, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6f3', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 2]], [[6, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 3]], [[-2, 3]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-3, 2]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[-1, 3]], [[0, 0]], [[0, 0]], [[1, 3]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 3]]]}
  • id: 21203922
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 58, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6f4', 'nt': [72, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 2]], [[-6, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 3]], [[0, 0]], [[3, 2]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[0, 0]], [[1, 3]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 3]], [[0, 0]], [[-1, 3]], [[0, 0]], [[0, 0]], [[1, 1]]]}
  • id: 21203923
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 59, 'cyclotomic_n': 24, 'dim': 6, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6g1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 6]], [[6, 6]], [[-2, 6]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6]], [[3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6]], [[-1, 6]], [[1, 6]], [[-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 1], [1, 5]], [[1, 3], [-2, 7]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 7]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 7]]]}
  • id: 21203925
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 60, 'cyclotomic_n': 24, 'dim': 6, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6g2', 'nt': [72, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 6]], [[-6, 6]], [[2, 6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6]], [[-3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6]], [[1, 6]], [[-1, 6]], [[1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[-1, 3], [2, 7]], [[0, 0]], [[1, 3], [-2, 7]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 7]], [[0, 0]], [[1, 3], [-2, 7]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]]]}
  • id: 21203926
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 61, 'cyclotomic_n': 24, 'dim': 6, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6g3', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-6, 6]], [[6, 6]], [[-2, 6]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 6]], [[3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 6]], [[-1, 6]], [[1, 6]], [[-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 7]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 1], [-1, 5]], [[-1, 3], [2, 7]], [[0, 0]], [[0, 0]], [[-1, 3], [2, 7]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 7]]]}
  • id: 21203927
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 62, 'cyclotomic_n': 24, 'dim': 6, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.665', 'image_order': 864, 'indicator': 0, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.2739.6g4', 'nt': [72, 4], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 6]], [[-6, 6]], [[2, 6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 6]], [[-3, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6]], [[1, 6]], [[-1, 6]], [[1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]], [[1, 3], [-2, 7]], [[0, 0]], [[-1, 3], [2, 7]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 5]], [[0, 0]], [[0, 0]], [[1, 3], [-2, 7]], [[0, 0]], [[-1, 3], [2, 7]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5]]]}
  • id: 21203928
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 63, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.386', 'image_order': 288, 'indicator': 1, 'kernel': '288.c1.a1', 'kernel_order': 6, 'label': '1728.2739.8a', 'nt': [24, 596], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203929
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 64, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '288.376', 'image_order': 288, 'indicator': -1, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.2739.8b', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203930
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 65, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.668', 'image_order': 864, 'indicator': 0, 'kernel': '864.c1.a1', 'kernel_order': 2, 'label': '1728.2739.12a1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203931
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 66, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.668', 'image_order': 864, 'indicator': 0, 'kernel': '864.c1.a1', 'kernel_order': 2, 'label': '1728.2739.12a2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[-2, 0], [-4, 1]], [[-2, 0], [-4, 1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203932
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 67, 'cyclotomic_n': 12, 'dim': 12, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.667', 'image_order': 864, 'indicator': -1, 'kernel': '864.b1.a1', 'kernel_order': 2, 'label': '1728.2739.12b1', 'nt': [144, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 21203933
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 68, 'cyclotomic_n': 12, 'dim': 12, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.2739', 'group_counter': 2739, 'group_order': 1728, 'image': None, 'image_isoclass': '864.667', 'image_order': 864, 'indicator': -1, 'kernel': '864.b1.a1', 'kernel_order': 2, 'label': '1728.2739.12b2', 'nt': [144, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[12, 0]], [[-12, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 89595599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 1728, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1728.2739.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.2739', 'subgroup_hash': 2739, 'subgroup_order': 1728, 'subgroup_tex': 'C_6.S_3^2:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 89595710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.1114', 'subgroup_hash': 1114, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times C_{12}).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 864, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.290', 'subgroup_hash': 290, 'subgroup_order': 864, 'subgroup_tex': '(C_3\\times C_{12}).D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 864, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.751', 'subgroup_hash': 751, 'subgroup_order': 864, 'subgroup_tex': '(C_2\\times \\He_3).\\OD_{16}', 'supersolvable': False, 'sylow': 0}
  • id: 89595803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 432, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.385', 'subgroup_hash': 385, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.321', 'subgroup_hash': 321, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.321', 'subgroup_hash': 321, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.139', 'subgroup_hash': 139, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 216, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.136', 'subgroup_hash': 136, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.95', 'subgroup_hash': 95, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.277', 'subgroup_hash': 277, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times \\He_3:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 89595622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, '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': '288.204', 'subgroup_hash': 204, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, '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': '288.524', 'subgroup_hash': 524, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 89595644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.113', 'subgroup_hash': 113, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.74', 'subgroup_hash': 74, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.71', 'subgroup_hash': 71, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 216, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.59', 'subgroup_hash': 59, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.59', 'subgroup_hash': 59, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.67', 'subgroup_hash': 67, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 54, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.14', 'subgroup_hash': 14, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.25', 'subgroup_hash': 25, 'subgroup_order': 216, 'subgroup_tex': '\\He_3:C_8', 'supersolvable': False, 'sylow': 0}
  • id: 89595777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.28', 'subgroup_hash': 28, 'subgroup_order': 192, 'subgroup_tex': '(C_2\\times C_4).D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595778
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595779
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.74', 'subgroup_hash': 74, 'subgroup_order': 144, 'subgroup_tex': 'C_6:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.90', 'subgroup_hash': 90, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 108, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 108, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 108, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.130', 'subgroup_hash': 130, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.37', 'subgroup_hash': 37, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.48', 'subgroup_hash': 48, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595807
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595808
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595810
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.p1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.12', 'subgroup_hash': 12, 'subgroup_order': 72, 'subgroup_tex': 'C_3:C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.13', 'subgroup_hash': 13, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1728.2739.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.5', 'subgroup_hash': 5, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.\\OD_{16}', 'supersolvable': True, 'sylow': 2}
  • id: 89595831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 54, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_8', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 54, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 54, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 27, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 89595839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 89595840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595848
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595849
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595601
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595602
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595603
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595604
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595606
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595615
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 27, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1728.2739.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 89595627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 24, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595634
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595635
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595638
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595643
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.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': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595651
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.x1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.y1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595660
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595661
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 155, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595662
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
  • id: 89595663
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595664
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595667
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.g1.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595672
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.h1.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595673
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.h1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595674
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.96.j1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595678
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595684
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595685
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 12, 'counter': 177, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.115', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 115, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595686
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595687
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595689
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595695
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595696
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595697
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595698
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595700
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595701
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595703
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595705
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595707
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595708
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595709
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.r1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595712
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 6, 'counter': 200, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595713
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 201, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595714
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595715
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595716
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595717
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595718
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595719
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595720
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 89595721
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.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': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 8, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.87', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 87, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 89595727
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595728
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595729
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595730
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595731
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595732
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595734
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595736
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595737
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
  • id: 89595738
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 224, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.374', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 374, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3^2:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595739
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 225, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.376', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 376, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4.\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595740
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 226, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.386', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 386, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595741
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595742
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595743
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.f1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595745
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.g1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595746
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.h1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595747
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.i1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595748
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.j1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595749
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.288.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.k1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595750
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.288.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.l1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595751
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.288.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595752
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 237, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.288.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.m1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 89595753
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.288.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595754
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.288.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.o1.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595756
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.288.o1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.o1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595757
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.2739.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.238', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 238, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6.\\SOPlus(4,2)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595758
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595759
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595760
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595761
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.432.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595762
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.432.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595763
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.2739.432.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f1.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 89595764
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.432.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.g1.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595765
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.432.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h1.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595767
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.432.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.i1.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 89595768
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 3, 'counter': 251, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.1910', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1910, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_6\\times C_{12}).D_4', 'simple': True, 'solvable': True, 'special_labels': ['D3', 'C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595769
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.576.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595770
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.576.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.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': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 89595771
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 254, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.864.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.665', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 665, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{12}.\\SOPlus(4,2)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 89595772
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 255, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.864.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.667', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 667, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{12}.\\SOPlus(4,2)', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 89595773
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 256, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.2739.864.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.668', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 668, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '(C_2^2\\times \\He_3).D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 89595774
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.864.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, '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: 89595775
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.2739.864.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 89595776
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.2739', 'ambient_counter': 2739, 'ambient_order': 1728, 'ambient_tex': 'C_6.S_3^2:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 1, 'counter': 259, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1728.2739.1728.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1728.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1728.2739', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2739, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6.S_3^2:C_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D4', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 89595599
    {'ambient': '1728.2739', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['1728.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8572, 3858, 6631, 3701, 8276, 6096, 8494, 4007], 'generators': [1, 576, 4, 96, 48, 8, 768, 1600, 2], 'label': '1728.2739.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.c1.a1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.238'}
  • id: 89595600
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4033', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.f1.a1', '12.i1.a1', '12.j1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5422, -1, 3716, -1, 5276, -1, 5766, -1], 'generators': [1422, 1344, 640, 48, 576, 4, 96], 'label': '1728.2739.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595601
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.b1.a1', '24.k1.a1', '24.k1.b1'], 'contains': ['96.b1.a1', '96.h1.a1', '96.h1.a2', '144.d1.a1', '144.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1033, -1, 1550, -1, 1228, -1, 1791, -1], 'generators': [200, 96, 576, 640], 'label': '1728.2739.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595602
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1'], 'contains': ['96.a1.a1', '96.i1.a1', '144.g1.a1', '144.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2085, -1, 5862, -1, 2231, -1, 3459, -1], 'generators': [396, 96, 576, 448], 'label': '1728.2739.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595603
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.b1.a1', '24.l1.a1', '24.l1.b1'], 'contains': ['96.b1.a1', '96.j1.a1', '96.j1.a2', '144.g1.a1', '144.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1236, -1, 1404, -1, 1074, -1, 1656, -1], 'generators': [204, 96, 576, 640], 'label': '1728.2739.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.f1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595604
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.g1.a1', '24.k1.a1', '24.l1.a1'], 'contains': ['96.b1.a1', '144.j1.a1', '144.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [465, -1, 360, -1, 367, -1, 457, -1], 'generators': [52, 64, 96, 576], 'label': '1728.2739.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595605
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.g1.a1', '24.k1.b1', '24.l1.b1'], 'contains': ['96.b1.a1', '144.j1.b1', '144.k1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [465, -1, 818, -1, 367, -1, 925, -1], 'generators': [48, 64, 96, 576], 'label': '1728.2739.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.g1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595606
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 32, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.h1.a1', '24.k1.a1', '24.l1.b1'], 'contains': ['96.b1.a1', '144.j1.a1', '144.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [257, -1, 179, -1, 208, -1, 182, -1], 'generators': [52, 96, 768, 576], 'label': '1728.2739.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595607
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 32, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.h1.a1', '24.k1.b1', '24.l1.a1'], 'contains': ['96.b1.a1', '144.j1.b1', '144.l1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [257, -1, 676, -1, 208, -1, 1064, -1], 'generators': [48, 96, 768, 576], 'label': '1728.2739.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.h1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595608
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.a1'], 'contains': ['96.c1.a1', '96.g1.a1', '96.i1.a1', '144.m1.a1', '144.n1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3935, -1, 7171, -1, 2539, -1, 3885, -1], 'generators': [100, 1416, 576, 448], 'label': '1728.2739.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.i1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595609
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.b1.a1'], 'contains': ['96.d1.a1', '96.h1.a1', '96.j1.a1', '144.m1.a1', '144.o1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1882, -1, 4888, -1, 1601, -1, 2884, -1], 'generators': [100, 1416, 576, 640], 'label': '1728.2739.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.j1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595610
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.b1.a1'], 'contains': ['96.d1.a1', '96.h1.a2', '96.j1.a2', '144.m1.a1', '144.o1.a2'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1882, -1, 5026, -1, 1601, -1, 3132, -1], 'generators': [100, 1416, 576, 1344], 'label': '1728.2739.48.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.j1.a2', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595611
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '8.k1.a1', '36.k1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8426, -1, 8349, -1, 8180, -1, 8410, -1], 'generators': [1691, 768, 1600, 96, 576, 1134, 4], 'label': '1728.2739.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.g1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 89595612
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.a1.a1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.e1.a1', '96.g1.a1', '96.i1.a1', '144.p1.a1', '144.q1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4302, -1, 7886, -1, 4359, -1, 4804, -1], 'generators': [4, 1416, 576, 448], 'label': '1728.2739.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.k1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595613
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.b1.a1', '24.o1.a1', '24.p1.a1'], 'contains': ['96.f1.a1', '96.h1.a1', '96.j1.a2', '144.p1.a1', '144.r1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3174, -1, 5725, -1, 3890, -1, 4260, -1], 'generators': [4, 1416, 576, 640], 'label': '1728.2739.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595614
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.b1.a1', '24.o1.a2', '24.p1.a2'], 'contains': ['96.f1.a1', '96.h1.a2', '96.j1.a1', '144.p1.a1', '144.r1.a2'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3174, -1, 6000, -1, 3890, -1, 4394, -1], 'generators': [4, 1416, 576, 1344], 'label': '1728.2739.48.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.l1.a2', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595615
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.c1.a1', '24.m1.a1', '24.r1.a1'], 'contains': ['96.e1.a1', '144.s1.a1', '144.v1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8476, -1, 8746, -1, 8349, -1, 8732, -1], 'generators': [2, 1600, 576, 4], 'label': '1728.2739.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.m1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595616
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.c1.a1', '24.n1.a1', '24.q1.a1'], 'contains': ['96.e1.a1', '144.s1.a1', '144.w1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8239, -1, 9184, -1, 8688, -1, 8569, -1], 'generators': [2, 832, 576, 4], 'label': '1728.2739.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.n1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595617
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.d1.a1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.e1.a1', '144.t1.a1', '144.x1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7559, -1, 8278, -1, 7970, -1, 8238, -1], 'generators': [1422, 576, 4, 448], 'label': '1728.2739.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '48.o1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595618
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.e1.a1', '24.o1.a1', '24.o1.a2'], 'contains': ['96.f1.a1', '144.s1.a1', '144.y1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6835, -1, 6773, -1, 7232, -1, 7591, -1], 'generators': [2, 64, 576, 4], 'label': '1728.2739.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.p1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595619
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.f1.a1', '24.o1.a1', '24.o1.a2'], 'contains': ['96.f1.a1', '144.t1.a1', '144.z1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5978, -1, 6941, -1, 6858, -1, 7264, -1], 'generators': [1422, 576, 4, 640], 'label': '1728.2739.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '48.q1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595620
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.i1.a1', '24.p1.a1', '24.p1.a2'], 'contains': ['96.f1.a1', '144.u1.a1', '144.ba1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5252, -1, 5317, -1, 4710, -1, 5112, -1], 'generators': [54, 64, 4, 576], 'label': '1728.2739.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.r1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595621
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 32, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.j1.a1', '24.p1.a1', '24.p1.a2'], 'contains': ['96.f1.a1', '144.u1.a1', '144.bb1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4644, -1, 4684, -1, 4869, -1, 5252, -1], 'generators': [54, 4, 768, 576], 'label': '1728.2739.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.s1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 89595622
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.f1.a1', '18.b1.a1', '18.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8977, -1, 9029, -1, 9207, -1, 9304, -1], 'generators': [1, 448, 4, 392, 576, 2, 96], 'label': '1728.2739.6.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595623
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.46', 'aut_weyl_index': 216, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7102, -1, 3794, -1, 6209, -1, 6517, -1], 'generators': [2, 1416, 816], 'label': '1728.2739.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 89595624
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '32.46', 'aut_weyl_index': 216, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.d1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9520, -1, 8307, -1, 9061, -1, 9177, -1], 'generators': [1, 1416], 'label': '1728.2739.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 89595625
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 216, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8899, -1, 8035, -1, 8932, -1, 9064, -1], 'generators': [1691, 1032], 'label': '1728.2739.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 89595626
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '64.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1'], 'contains': ['192.a1.a1', '192.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2763, 5387, 6498, 4877, 2168, 5012, 3100, 4791], 'generators': [64, 768], 'label': '1728.2739.64.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.b1.a1', '32.a1.a1', '32.c1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '1728.2739', 'quotient_action_image': '8.3', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595627
    {'ambient': '1728.2739', 'aut_centralizer_order': 864, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.e1.a1', '36.a1.a1', '36.h1.a1', '36.i1.a1'], 'contains': ['144.a1.a1', '144.s1.a1', '216.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7854, 1259, 7319, 1139, 7597, 8523, 7754, 1419], 'generators': [2, 96, 576, 4], 'label': '1728.2739.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '432.238', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595628
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.g1.a1', '144.m1.a1', '144.p1.a1', '216.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3765, -1, 4462, -1, 3629, -1, 4114, -1], 'generators': [4, 1416, 96, 576], 'label': '1728.2739.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595629
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.a1'], 'contains': ['144.b1.a1', '144.e1.a1', '144.h1.a1', '144.n1.a1', '144.q1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4436, -1, 8125, -1, 4525, -1, 4950, -1], 'generators': [4, 392, 96, 448], 'label': '1728.2739.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595630
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1'], 'contains': ['144.c1.a1', '144.f1.a1', '144.i1.a1', '144.o1.a1', '144.o1.a2', '144.r1.a1', '144.r1.a2', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2399, -1, 3301, -1, 3451, -1, 3739, -1], 'generators': [4, 200, 96, 640], 'label': '1728.2739.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595631
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.f1.a1', '36.a1.a1', '36.j1.a1', '36.k1.a1'], 'contains': ['144.a1.a1', '144.t1.a1', '216.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7428, -1, 7563, -1, 7046, -1, 7429, -1], 'generators': [1422, 96, 576, 4], 'label': '1728.2739.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595632
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '36.b1.a1', '36.h1.a1', '36.j1.a1'], 'contains': ['144.a1.a1', '144.j1.a1', '144.j1.b1', '216.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2911, -1, 2285, -1, 3266, -1, 2621, -1], 'generators': [4, 48, 96, 576], 'label': '1728.2739.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595633
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '18.a1.a1', '18.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5817, -1, 3409, -1, 5529, -1, 5987, -1], 'generators': [2, 640, 96, 200, 576, 816, 4], 'label': '1728.2739.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '6.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595634
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.j1.a1', '36.c1.a1', '36.h1.a1', '36.j1.a1'], 'contains': ['144.a1.a1', '144.u1.a1', '216.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6925, -1, 4005, -1, 5558, -1, 5990, -1], 'generators': [54, 96, 4, 576], 'label': '1728.2739.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.g1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595635
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.d1.a1', '36.l1.a1', '36.m1.a1'], 'contains': ['144.b1.a1', '144.v1.a1', '144.w1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9386, -1, 9444, -1, 9028, -1, 9164, -1], 'generators': [2, 96, 1600, 4], 'label': '1728.2739.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595636
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.d1.a1'], 'contains': ['144.b1.a1', '144.x1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8179, -1, 8793, -1, 8161, -1, 8405, -1], 'generators': [398, 96, 4, 448], 'label': '1728.2739.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595637
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.e1.a1', '36.n1.a1', '36.o1.a1'], 'contains': ['144.c1.a1', '144.y1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6510, -1, 2608, -1, 6517, -1, 6830, -1], 'generators': [2, 96, 64, 4], 'label': '1728.2739.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.j1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595638
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.e1.a1', '36.p1.a1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.z1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5699, -1, 3503, -1, 6329, -1, 6665, -1], 'generators': [206, 96, 4, 640], 'label': '1728.2739.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '72.k1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595639
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.f1.a1', '36.n1.a1', '36.p1.a1'], 'contains': ['144.c1.a1', '144.k1.a1', '144.k1.b1', '216.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2631, -1, 1832, -1, 3078, -1, 2133, -1], 'generators': [4, 48, 64, 96], 'label': '1728.2739.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.l1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595640
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.f1.a1', '36.o1.a1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.l1.a1', '144.l1.b1', '216.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2210, -1, 2000, -1, 2890, -1, 2297, -1], 'generators': [4, 48, 96, 768], 'label': '1728.2739.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.m1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595641
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '72.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.g1.a1', '36.n1.a1', '36.q1.a1'], 'contains': ['144.c1.a1', '144.ba1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5507, -1, 2891, -1, 5370, -1, 5826, -1], 'generators': [54, 96, 64, 4], 'label': '1728.2739.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.n1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595642
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '36.g1.a1', '36.o1.a1', '36.p1.a1'], 'contains': ['144.c1.a1', '144.bb1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4801, -1, 3059, -1, 5749, -1, 6157, -1], 'generators': [54, 96, 4, 768], 'label': '1728.2739.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.o1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595643
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.38', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.b1.a1'], 'contains': ['144.d1.a1', '144.j1.a1', '216.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [536, -1, 1301, -1, 902, -1, 1339, -1], 'generators': [820, 1416, 96, 576], 'label': '1728.2739.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.p1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 89595644
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.e1.a1', '16.f1.a1', '24.a1.a1', '24.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3330, 5912, 4972, 5351, 3488, 4091, 3943, 5675], 'generators': [4, 576, 1344, 1416, 96, 640], 'label': '1728.2739.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.b1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595645
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.38', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '36.b1.a1'], 'contains': ['144.d1.a1', '144.j1.b1', '216.f1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [536, -1, 1547, -1, 902, -1, 1506, -1], 'generators': [1416, 816, 96, 576], 'label': '1728.2739.72.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.p1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.b1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 89595646
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.f1.a1'], 'contains': ['144.f1.a1', '144.k1.a1', '144.l1.a1', '216.f1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [68, -1, 230, -1, 539, -1, 306, -1], 'generators': [820, 200, 96, 640], 'label': '1728.2739.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.q1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595647
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '36.f1.a1'], 'contains': ['144.f1.a1', '144.k1.b1', '144.l1.b1', '216.f1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [68, -1, 1069, -1, 539, -1, 1188, -1], 'generators': [200, 816, 96, 640], 'label': '1728.2739.72.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.q1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595648
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.38', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.l1.b1', '36.b1.a1'], 'contains': ['144.g1.a1', '144.j1.a1', '144.j1.b1', '216.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [731, -1, 76, -1, 712, -1, 758, -1], 'generators': [76, 48, 96, 576], 'label': '1728.2739.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595649
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.f1.a1'], 'contains': ['144.i1.a1', '144.k1.a1', '144.l1.b1', '216.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [360, -1, 794, -1, 67, -1, 607, -1], 'generators': [1420, 48, 96, 1344], 'label': '1728.2739.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.s1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595650
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '36.f1.a1'], 'contains': ['144.i1.a1', '144.k1.b1', '144.l1.a1', '216.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [360, -1, 932, -1, 67, -1, 58, -1], 'generators': [76, 48, 96, 64], 'label': '1728.2739.72.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.s1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595651
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.n1.a1', '24.o1.a1', '24.o1.a2', '36.a1.a1'], 'contains': ['144.p1.a1', '144.s1.a1', '144.t1.a1', '216.h1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7663, -1, 7924, -1, 7782, -1, 8073, -1], 'generators': [2, 1416, 576, 4], 'label': '1728.2739.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.t1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595652
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.p1.a2', '36.c1.a1'], 'contains': ['144.p1.a1', '144.u1.a1', '216.i1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5938, -1, 4627, -1, 5182, -1, 5391, -1], 'generators': [822, 1416, 4, 576], 'label': '1728.2739.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '72.u1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595653
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.d1.a1'], 'contains': ['144.q1.a1', '144.v1.a1', '144.x1.a1', '216.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8882, -1, 9114, -1, 8518, -1, 9015, -1], 'generators': [2, 1416, 4, 448], 'label': '1728.2739.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.v1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595654
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.d1.a1'], 'contains': ['144.q1.a1', '144.w1.a1', '144.x1.a1', '216.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8635, -1, 9251, -1, 8858, -1, 8881, -1], 'generators': [2, 1416, 4, 1408], 'label': '1728.2739.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.w1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595655
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '24.c1.a1', '24.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7142, 1259, 8339, 1139, 7355, 8523, 7442, 1419], 'generators': [2, 576, 4, 96, 64, 768], 'label': '1728.2739.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595656
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.e1.a1'], 'contains': ['144.r1.a1', '144.y1.a1', '144.z1.a1', '216.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6291, -1, 5014, -1, 6686, -1, 6978, -1], 'generators': [2, 1416, 4, 640], 'label': '1728.2739.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.x1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595657
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a2', '36.e1.a1'], 'contains': ['144.r1.a2', '144.y1.a1', '144.z1.a1', '216.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6291, -1, 5501, -1, 6686, -1, 7113, -1], 'generators': [2, 1416, 4, 1344], 'label': '1728.2739.72.x1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.x1.a2', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595658
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.g1.a1'], 'contains': ['144.r1.a1', '144.ba1.a1', '144.bb1.a1', '216.i1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5066, -1, 4314, -1, 5010, -1, 5542, -1], 'generators': [822, 1416, 4, 640], 'label': '1728.2739.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1.a1', 'old_label': '72.y1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595659
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a2', '36.g1.a1'], 'contains': ['144.r1.a2', '144.ba1.a1', '144.bb1.a1', '216.i1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5066, -1, 3813, -1, 5010, -1, 5677, -1], 'generators': [54, 1416, 4, 1344], 'label': '1728.2739.72.y1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1.a1', 'old_label': '72.y1.a2', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595660
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.r1.a1', '36.i1.a1'], 'contains': ['144.s1.a1', '216.j1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9192, -1, 9856, -1, 9429, -1, 9651, -1], 'generators': [1, 2, 4, 576], 'label': '1728.2739.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.z1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595661
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '36.k1.a1'], 'contains': ['144.t1.a1', '216.k1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8504, -1, 8962, -1, 9171, -1, 9290, -1], 'generators': [1691, 576, 1134, 4], 'label': '1728.2739.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '72.ba1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595662
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.l1.a1'], 'contains': ['144.w1.a1', '216.j1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9827, -1, 9765, -1, 9791, -1, 9741, -1], 'generators': [1, 1408, 2, 4], 'label': '1728.2739.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1.a1', 'old_label': '72.bb1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595663
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '36.m1.a1'], 'contains': ['144.v1.a1', '216.j1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9932, -1, 9950, -1, 9688, -1, 9831, -1], 'generators': [1, 2, 4, 1600], 'label': '1728.2739.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1.a1', 'old_label': '72.bc1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595664
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.c1.a1', '48.e1.a1'], 'contains': ['192.a1.a1', '288.a1.a1', '288.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2110, -1, 4953, -1, 2596, -1, 3547, -1], 'generators': [96, 1600, 576], 'label': '1728.2739.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.a1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595665
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.b1.a1', '48.d1.a1', '48.f1.a1', '48.g1.a1', '48.g1.b1', '48.h1.a1', '48.h1.b1'], 'contains': ['192.b1.a1', '288.a1.a1', '288.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1040, -1, 564, -1, 1266, -1, 1760, -1], 'generators': [96, 64, 576], 'label': '1728.2739.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595666
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '24.d1.a1', '24.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6214, 3736, 7898, 3382, 7075, 6163, 7197, 3685], 'generators': [1422, 576, 1344, 96, 4, 640], 'label': '1728.2739.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595667
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.i1.a1'], 'contains': ['192.a1.a1', '288.b1.a1', '288.f1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4717, -1, 7232, -1, 3060, -1, 3953, -1], 'generators': [100, 1600, 576], 'label': '1728.2739.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.c1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595668
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.b1.a1', '48.j1.a1', '48.j1.a2'], 'contains': ['192.b1.a1', '288.b1.a1', '288.g1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2973, -1, 5246, -1, 2286, -1, 3275, -1], 'generators': [100, 64, 576], 'label': '1728.2739.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.d1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595669
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.a1', '48.k1.a1', '48.m1.a1', '48.n1.a1', '48.o1.a1'], 'contains': ['192.a1.a1', '288.c1.a1', '288.h1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5496, -1, 8430, -1, 4425, -1, 5073, -1], 'generators': [4, 1600, 576], 'label': '1728.2739.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.e1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595670
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.b1.a1', '48.l1.a1', '48.l1.a2', '48.p1.a1', '48.q1.a1', '48.r1.a1', '48.s1.a1'], 'contains': ['192.b1.a1', '288.c1.a1', '288.i1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4070, -1, 6401, -1, 4270, -1, 4937, -1], 'generators': [4, 64, 576], 'label': '1728.2739.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '96.f1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595671
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.c1.a1', '48.i1.a1', '48.k1.a1'], 'contains': ['192.a1.a1', '288.j1.a1', '288.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3176, -1, 6918, -1, 2905, -1, 3817, -1], 'generators': [1416, 576, 448], 'label': '1728.2739.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.g1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595672
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.d1.a1', '48.j1.a1', '48.l1.a1'], 'contains': ['192.b1.a1', '288.j1.a1', '288.l1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1527, -1, 5871, -1, 1967, -1, 2789, -1], 'generators': [1416, 576, 640], 'label': '1728.2739.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.h1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595673
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.d1.a1', '48.j1.a2', '48.l1.a2'], 'contains': ['192.b1.a1', '288.j1.a1', '288.l1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1527, -1, 6146, -1, 1967, -1, 2924, -1], 'generators': [1416, 576, 1344], 'label': '1728.2739.96.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.h1.a2', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595674
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.e1.a1', '48.i1.a1', '48.k1.a1'], 'contains': ['192.a1.a1', '288.m1.a1', '288.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3468, -1, 7055, -1, 2751, -1, 3683, -1], 'generators': [1420, 576, 448], 'label': '1728.2739.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '96.i1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595675
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.f1.a1', '48.j1.a1', '48.l1.a2'], 'contains': ['192.b1.a1', '288.m1.a1', '288.o1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1685, -1, 6008, -1, 1813, -1, 2520, -1], 'generators': [1420, 576, 1344], 'label': '1728.2739.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.j1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595676
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.f1.a1', '48.j1.a2', '48.l1.a1'], 'contains': ['192.b1.a1', '288.m1.a1', '288.o1.a2'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1685, -1, 5733, -1, 1813, -1, 2655, -1], 'generators': [1420, 576, 640], 'label': '1728.2739.96.j1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.j1.a2', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595677
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '864.2282', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['216.j1.a1', '216.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '24.k1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1188, 8460, 1022, 7156, 1740, 1923, 1590, 7499], 'generators': [52, 576, 1344, 1416, 96, 640], 'label': '1728.2739.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '864.665', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '432.238'}
  • id: 89595678
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1', '36.e1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8477, -1, 7467, -1, 7414, -1, 7914, -1], 'generators': [2, 1416, 96], 'label': '1728.2739.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595679
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.11', 'aut_weyl_index': 432, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.f1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.d1.a1', '216.f1.a1', '216.f1.b1', '216.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1565, -1, 1869, -1, 2705, -1, 2459, -1], 'generators': [4, 1416, 816], 'label': '1728.2739.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 89595680
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.11', 'aut_weyl_index': 432, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.g1.a1', '54.a1.a1'], 'contains': ['216.b1.a1', '216.e1.a1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6044, -1, 3608, -1, 5933, -1, 6319, -1], 'generators': [822, 1416, 96], 'label': '1728.2739.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 89595681
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '36.o1.a1', '54.a1.a1'], 'contains': ['216.a1.a1', '216.d1.a1', '216.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6628, -1, 2505, -1, 6180, -1, 6535, -1], 'generators': [2, 48], 'label': '1728.2739.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595682
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.l1.a1', '36.m1.a1', '54.b1.a1'], 'contains': ['216.a1.a1', '216.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9622, -1, 9643, -1, 9559, -1, 9538, -1], 'generators': [1, 96], 'label': '1728.2739.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595683
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '36.p1.a1', '36.q1.a1', '54.a1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6986, -1, 2788, -1, 6076, -1, 6443, -1], 'generators': [74, 48], 'label': '1728.2739.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595684
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '54.c1.a1'], 'contains': ['216.c1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8781, -1, 8372, -1, 9299, -1, 9402, -1], 'generators': [1691, 96], 'label': '1728.2739.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '108.g1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595703
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '72.c1.a1'], 'contains': ['288.f1.a1', '288.k1.a1', '288.n1.a1', '432.e1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4274, -1, 7881, -1, 3342, -1, 4418, -1], 'generators': [100, 1416, 448], 'label': '1728.2739.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.n1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595685
    {'ambient': '1728.2739', 'aut_centralizer_order': 3456, 'aut_label': '144.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '72.a1.a1', '72.b1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1'], 'contains': ['288.a1.a1', '288.b1.a1', '288.c1.a1', '432.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4774, 2488, 4885, 2252, 3960, 8130, 4666, 1796], 'generators': [4, 96, 576], 'label': '1728.2739.144.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['16.a1.a1', '72.a1.a1'], 'normal_contains': ['288.b1.a1', '288.a1.a1', '288.c1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.238', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.45', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595686
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.c1.a1', '72.h1.a1', '72.i1.a1'], 'contains': ['288.d1.a1', '288.f1.a1', '288.h1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5898, -1, 8423, -1, 4580, -1, 5209, -1], 'generators': [4, 96, 1600], 'label': '1728.2739.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595687
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.d1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1'], 'contains': ['288.e1.a1', '288.g1.a1', '288.i1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3728, -1, 3192, -1, 3723, -1, 4233, -1], 'generators': [4, 96, 64], 'label': '1728.2739.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595688
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '864.2282', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': ['216.j1.a1', '216.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.a1', '16.d1.b1', '24.k1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1188, 8460, 1471, 8861, 1740, 1923, 1986, 9222], 'generators': [1416, 576, 1344, 48, 96, 640], 'label': '1728.2739.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '864.665', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '432.238'}
  • id: 89595689
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '72.b1.a1', '72.p1.a1', '72.p1.b1'], 'contains': ['288.a1.a1', '288.j1.a1', '432.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1271, -1, 1864, -1, 1658, -1, 2248, -1], 'generators': [1416, 96, 576], 'label': '1728.2739.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595690
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.c1.a1'], 'contains': ['288.d1.a1', '288.k1.a1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2490, -1, 6669, -1, 3260, -1, 4129, -1], 'generators': [392, 96, 448], 'label': '1728.2739.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595691
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '72.d1.a1', '72.q1.a1', '72.q1.b1'], 'contains': ['288.e1.a1', '288.l1.a1', '288.l1.a2', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [915, -1, 1283, -1, 1385, -1, 2004, -1], 'generators': [200, 96, 640], 'label': '1728.2739.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.f1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595692
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.f1.a1', '72.b1.a1', '72.r1.a1'], 'contains': ['288.a1.a1', '288.m1.a1', '432.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1622, -1, 1686, -1, 1503, -1, 2113, -1], 'generators': [1420, 96, 576], 'label': '1728.2739.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.g1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595693
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '72.c1.a1'], 'contains': ['288.d1.a1', '288.n1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2406, -1, 6742, -1, 3178, -1, 4057, -1], 'generators': [396, 96, 448], 'label': '1728.2739.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.h1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595694
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.d1.a1', '72.s1.a1', '72.s1.b1'], 'contains': ['288.e1.a1', '288.o1.a1', '288.o1.a2', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1145, -1, 1163, -1, 1148, -1, 1656, -1], 'generators': [204, 96, 640], 'label': '1728.2739.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.i1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595695
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.h1.a1', '72.f1.a1', '72.p1.a1', '72.r1.a1'], 'contains': ['288.a1.a1', '432.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [583, -1, 50, -1, 900, -1, 1098, -1], 'generators': [52, 96, 576], 'label': '1728.2739.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.j1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595696
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.b1', '48.h1.b1', '72.f1.a1', '72.p1.b1', '72.r1.a1'], 'contains': ['288.a1.a1', '432.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [583, -1, 487, -1, 900, -1, 1506, -1], 'generators': [48, 96, 576], 'label': '1728.2739.144.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.j1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595697
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '72.l1.a1', '72.q1.a1', '72.s1.a1'], 'contains': ['288.e1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [291, -1, 262, -1, 642, -1, 754, -1], 'generators': [52, 64, 96], 'label': '1728.2739.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.k1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595698
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.b1', '72.l1.a1', '72.q1.b1', '72.s1.b1'], 'contains': ['288.e1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [291, -1, 944, -1, 642, -1, 1188, -1], 'generators': [48, 64, 96], 'label': '1728.2739.144.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.k1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595699
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.545', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '24.g1.a1', '24.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2588, -1, 2276, -1, 3153, -1, 2479, -1], 'generators': [4, 576, 768, 48, 64, 96], 'label': '1728.2739.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595700
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '72.m1.a1', '72.q1.a1', '72.s1.b1'], 'contains': ['288.e1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 354, -1, 539, -1, 426, -1], 'generators': [52, 96, 768], 'label': '1728.2739.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.l1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595701
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.b1', '72.m1.a1', '72.q1.b1', '72.s1.a1'], 'contains': ['288.e1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 785, -1, 539, -1, 1278, -1], 'generators': [48, 96, 768], 'label': '1728.2739.144.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '144.l1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595702
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.j1.a1', '48.j1.a2', '72.b1.a1'], 'contains': ['288.b1.a1', '288.j1.a1', '288.m1.a1', '432.e1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3150, -1, 5480, -1, 2441, -1, 3411, -1], 'generators': [100, 1416, 576], 'label': '1728.2739.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.m1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595704
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '72.d1.a1'], 'contains': ['288.g1.a1', '288.l1.a1', '288.o1.a1', '432.e1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2278, -1, 3835, -1, 2086, -1, 3028, -1], 'generators': [100, 1416, 640], 'label': '1728.2739.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.o1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595705
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a2', '72.d1.a1'], 'contains': ['288.g1.a1', '288.l1.a2', '288.o1.a2', '432.e1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2278, -1, 4517, -1, 2086, -1, 3172, -1], 'generators': [100, 1416, 1344], 'label': '1728.2739.144.o1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.o1.a2', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595706
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.l1.a1', '48.l1.a2', '72.b1.a1', '72.t1.a1', '72.u1.a1'], 'contains': ['288.c1.a1', '288.j1.a1', '288.m1.a1', '432.f1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4108, -1, 6446, -1, 4115, -1, 4801, -1], 'generators': [4, 1416, 576], 'label': '1728.2739.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.p1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595707
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '72.c1.a1', '72.v1.a1', '72.w1.a1'], 'contains': ['288.h1.a1', '288.k1.a1', '288.n1.a1', '432.f1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4536, -1, 8663, -1, 4698, -1, 5313, -1], 'generators': [4, 1416, 448], 'label': '1728.2739.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.q1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595708
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '72.d1.a1', '72.x1.a1', '72.y1.a1'], 'contains': ['288.i1.a1', '288.l1.a1', '288.o1.a2', '432.f1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3272, -1, 4741, -1, 3841, -1, 4490, -1], 'generators': [4, 1416, 640], 'label': '1728.2739.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.r1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595709
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a2', '72.d1.a1', '72.x1.a2', '72.y1.a2'], 'contains': ['288.i1.a1', '288.l1.a2', '288.o1.a1', '432.f1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3272, -1, 4668, -1, 3841, -1, 4562, -1], 'generators': [4, 1416, 1344], 'label': '1728.2739.144.r1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '144.r1.a2', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595710
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.30413', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.f1.a1', '6.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5817, 5629, 3716, 5351, 5529, 4360, 5987, 5675], 'generators': [2, 96, 640, 1416, 4, 576, 1344, 48], 'label': '1728.2739.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.238'}
  • id: 89595711
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.545', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '24.i1.a1', '24.j1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5106, -1, 4115, -1, 4574, -1, 5059, -1], 'generators': [54, 576, 768, 96, 64, 4], 'label': '1728.2739.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595712
    {'ambient': '1728.2739', 'aut_centralizer_order': 864, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.n1.a1', '48.p1.a1', '72.a1.a1', '72.t1.a1', '72.z1.a1'], 'contains': ['288.c1.a1', '432.g1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7900, -1, 8210, -1, 7789, -1, 8089, -1], 'generators': [2, 576, 4], 'label': '1728.2739.144.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.s1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595713
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.q1.a1', '72.e1.a1', '72.t1.a1', '72.ba1.a1'], 'contains': ['288.c1.a1', '432.h1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7540, -1, 8004, -1, 7534, -1, 8001, -1], 'generators': [1422, 576, 4], 'label': '1728.2739.144.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '144.t1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595714
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.s1.a1', '72.g1.a1', '72.u1.a1'], 'contains': ['288.c1.a1', '432.i1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6279, -1, 5002, -1, 4892, -1, 5394, -1], 'generators': [54, 4, 576], 'label': '1728.2739.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '144.u1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595715
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '72.h1.a1', '72.v1.a1', '72.bc1.a1'], 'contains': ['288.h1.a1', '432.g1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9118, -1, 9078, -1, 8433, -1, 8874, -1], 'generators': [2, 1600, 4], 'label': '1728.2739.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.v1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595716
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '72.h1.a1', '72.w1.a1', '72.bb1.a1'], 'contains': ['288.h1.a1', '432.g1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9015, -1, 9347, -1, 8774, -1, 8607, -1], 'generators': [2, 832, 4], 'label': '1728.2739.144.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.w1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595717
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '72.i1.a1', '72.v1.a1', '72.w1.a1'], 'contains': ['288.h1.a1', '432.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8109, -1, 8909, -1, 8065, -1, 8321, -1], 'generators': [1422, 4, 448], 'label': '1728.2739.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '144.x1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595718
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '72.j1.a1', '72.x1.a1', '72.x1.a2'], 'contains': ['288.i1.a1', '432.g1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5723, -1, 5142, -1, 6738, -1, 7091, -1], 'generators': [2, 64, 4], 'label': '1728.2739.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '144.y1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595719
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '72.k1.a1', '72.x1.a1', '72.x1.a2'], 'contains': ['288.i1.a1', '432.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5574, -1, 5596, -1, 6635, -1, 6989, -1], 'generators': [1422, 4, 640], 'label': '1728.2739.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '144.z1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595720
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '72.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '72.n1.a1', '72.y1.a1', '72.y1.a2'], 'contains': ['288.i1.a1', '432.i1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5172, -1, 4186, -1, 4789, -1, 5484, -1], 'generators': [54, 64, 4], 'label': '1728.2739.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1.a1', 'old_label': '144.ba1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595721
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '72.o1.a1', '72.y1.a1', '72.y1.a2'], 'contains': ['288.i1.a1', '432.i1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4906, -1, 4056, -1, 4997, -1, 5574, -1], 'generators': [54, 4, 768], 'label': '1728.2739.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1.a1', 'old_label': '144.bb1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595722
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.2282', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.d1.b1', '24.l1.a1', '24.l1.b1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1408, -1, 1244, -1, 1286, -1, 1336, -1], 'generators': [1420, 576, 1344, 48, 96, 640], 'label': '1728.2739.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595723
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.c1.a1', '96.e1.a1', '96.g1.a1', '96.i1.a1'], 'contains': ['576.a1.a1', '576.b1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3449, -1, 7035, -1, 2866, -1, 3749, -1], 'generators': [1600, 576], 'label': '1728.2739.192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '192.a1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595724
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.a1', '96.d1.a1', '96.f1.a1', '96.h1.a1', '96.h1.a2', '96.j1.a1', '96.j1.a2'], 'contains': ['576.a1.a1', '576.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1971, -1, 5929, -1, 2255, -1, 3095, -1], 'generators': [64, 576], 'label': '1728.2739.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595725
    {'ambient': '1728.2739', 'aut_centralizer_order': 1728, 'aut_label': '216.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.h1.a1', '72.j1.a1', '108.a1.a1', '108.d1.a1', '108.e1.a1'], 'contains': ['432.a1.a1', '432.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8268, 1581, 7328, 1432, 7406, 9434, 7754, 544], 'generators': [2, 96], 'label': '1728.2739.216.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '432.238', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.17', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595726
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.c1.a1', '72.d1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '432.e1.a1', '432.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3779, -1, 3754, -1, 3599, -1, 4341, -1], 'generators': [4, 1416, 96], 'label': '1728.2739.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595727
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.i1.a1', '72.k1.a1', '108.a1.a1', '108.f1.a1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7641, -1, 7467, -1, 7152, -1, 7524, -1], 'generators': [1422, 96], 'label': '1728.2739.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595728
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.l1.a1', '72.m1.a1', '108.b1.a1', '108.d1.a1', '108.f1.a1'], 'contains': ['432.a1.a1', '432.d1.a1', '432.d1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2747, -1, 2030, -1, 3461, -1, 2384, -1], 'generators': [4, 48], 'label': '1728.2739.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595729
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.n1.a1', '72.o1.a1', '108.c1.a1', '108.d1.a1', '108.f1.a1'], 'contains': ['432.a1.a1', '432.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6088, -1, 3085, -1, 5653, -1, 6073, -1], 'generators': [54, 96], 'label': '1728.2739.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595730
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.3', 'aut_weyl_index': 864, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1.a1', '72.q1.a1', '108.b1.a1'], 'contains': ['432.b1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [552, -1, 1145, -1, 1029, -1, 1392, -1], 'generators': [820, 1416], 'label': '1728.2739.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 89595731
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.3', 'aut_weyl_index': 864, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.p1.b1', '72.q1.b1', '108.b1.a1'], 'contains': ['432.b1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [552, -1, 1582, -1, 1029, -1, 1896, -1], 'generators': [1416, 816], 'label': '1728.2739.216.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.f1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 89595732
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.3', 'aut_weyl_index': 864, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1.a1', '72.s1.a1', '72.s1.b1', '108.b1.a1'], 'contains': ['432.c1.a1', '432.d1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [976, -1, 541, -1, 770, -1, 985, -1], 'generators': [76, 48], 'label': '1728.2739.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '216.g1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595733
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 192, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.f1.a1', '16.g1.a1', '16.h1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.o1.a2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6809, -1, 8107, -1, 7615, -1, 7670, -1], 'generators': [2, 576, 1344, 1416, 4, 640], 'label': '1728.2739.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 89595734
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.a1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.x1.a2', '108.a1.a1'], 'contains': ['432.f1.a1', '432.g1.a1', '432.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8426, -1, 7760, -1, 7662, -1, 7889, -1], 'generators': [2, 1416], 'label': '1728.2739.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.h1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595735
    {'ambient': '1728.2739', 'aut_centralizer_order': 16, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.u1.a1', '72.y1.a1', '72.y1.a2', '108.c1.a1'], 'contains': ['432.f1.a1', '432.i1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5543, -1, 4159, -1, 5127, -1, 5688, -1], 'generators': [822, 1416], 'label': '1728.2739.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1.a1', 'old_label': '216.i1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595736
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1.a1', '72.bb1.a1', '72.bc1.a1', '108.e1.a1'], 'contains': ['432.g1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9622, -1, 9851, -1, 9559, -1, 9651, -1], 'generators': [1], 'label': '1728.2739.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1.a1', 'old_label': '216.j1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595737
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1728, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1.a1', '108.g1.a1'], 'contains': ['432.h1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8635, -1, 8624, -1, 9171, -1, 9290, -1], 'generators': [1691], 'label': '1728.2739.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '216.k1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595738
    {'ambient': '1728.2739', 'aut_centralizer_order': 3456, 'aut_label': '288.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '144.a1.a1', '144.d1.a1', '144.g1.a1', '144.j1.a1', '144.j1.b1'], 'contains': ['576.a1.a1', '864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1482, 4934, 1857, 4467, 1785, 6010, 2189, 3832], 'generators': [96, 576], 'label': '1728.2739.288.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['32.a1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '864.665', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.130', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595739
    {'ambient': '1728.2739', 'aut_centralizer_order': 3456, 'aut_label': '288.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.d1.a1', '144.a1.a1', '144.m1.a1'], 'contains': ['576.a1.a1', '864.b1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4138, 4068, 5386, 2853, 2740, 6700, 3541, 2506], 'generators': [100, 576], 'label': '1728.2739.288.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['32.b1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1', '864.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '864.667', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.131', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595740
    {'ambient': '1728.2739', 'aut_centralizer_order': 3456, 'aut_label': '288.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.f1.a1', '144.a1.a1', '144.p1.a1', '144.s1.a1', '144.t1.a1', '144.u1.a1'], 'contains': ['576.a1.a1', '864.c1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4809, 3152, 6723, 3683, 4425, 7391, 5057, 3169], 'generators': [4, 576], 'label': '1728.2739.288.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '288.c1.a1', 'normal_contained_in': ['32.c1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1', '864.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '864.668', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.136', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595741
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '144.b1.a1', '144.e1.a1', '144.h1.a1'], 'contains': ['576.b1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2705, -1, 6836, -1, 3096, -1, 3985, -1], 'generators': [96, 1600], 'label': '1728.2739.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '288.d1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595742
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '144.c1.a1', '144.f1.a1', '144.i1.a1', '144.k1.a1', '144.k1.b1', '144.l1.a1', '144.l1.b1'], 'contains': ['576.c1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [830, -1, 921, -1, 1326, -1, 1656, -1], 'generators': [96, 64], 'label': '1728.2739.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.e1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595743
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '144.b1.a1', '144.n1.a1'], 'contains': ['576.b1.a1', '864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4938, -1, 7965, -1, 3342, -1, 4201, -1], 'generators': [100, 1600], 'label': '1728.2739.288.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '288.f1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595744
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.530', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.f1.a1', '16.i1.a1', '24.p1.a1', '24.p1.a2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4866, -1, 5214, -1, 4289, -1, 4779, -1], 'generators': [54, 576, 1344, 1416, 4, 640], 'label': '1728.2739.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.i1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 89595745
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '144.c1.a1', '144.o1.a1', '144.o1.a2'], 'contains': ['576.c1.a1', '864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2493, -1, 4342, -1, 2564, -1, 3387, -1], 'generators': [100, 64], 'label': '1728.2739.288.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.g1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595746
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '144.b1.a1', '144.q1.a1', '144.v1.a1', '144.w1.a1', '144.x1.a1'], 'contains': ['576.b1.a1', '864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6297, -1, 8764, -1, 4639, -1, 5261, -1], 'generators': [4, 1600], 'label': '1728.2739.288.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '288.h1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595747
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '144.c1.a1', '144.r1.a1', '144.r1.a2', '144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1'], 'contains': ['576.c1.a1', '864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4726, -1, 5023, -1, 4343, -1, 4953, -1], 'generators': [4, 64], 'label': '1728.2739.288.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.i1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595748
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.h1.a1', '96.h1.a2', '144.d1.a1', '144.m1.a1', '144.p1.a1'], 'contains': ['576.a1.a1', '864.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2364, -1, 6230, -1, 2482, -1, 3315, -1], 'generators': [1416, 576], 'label': '1728.2739.288.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '288.j1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595749
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '144.e1.a1', '144.n1.a1', '144.q1.a1'], 'contains': ['576.b1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3483, -1, 7239, -1, 3260, -1, 4129, -1], 'generators': [1416, 448], 'label': '1728.2739.288.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '288.k1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595750
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '144.f1.a1', '144.o1.a1', '144.r1.a1'], 'contains': ['576.c1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1743, -1, 4814, -1, 2168, -1, 3018, -1], 'generators': [1416, 640], 'label': '1728.2739.288.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.l1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595751
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a2', '144.f1.a1', '144.o1.a2', '144.r1.a2'], 'contains': ['576.c1.a1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1743, -1, 4590, -1, 2168, -1, 3172, -1], 'generators': [1416, 1344], 'label': '1728.2739.288.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.l1.a2', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595752
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.j1.a1', '96.j1.a2', '144.g1.a1', '144.m1.a1', '144.p1.a1'], 'contains': ['576.a1.a1', '864.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2576, -1, 5806, -1, 2400, -1, 3243, -1], 'generators': [1420, 576], 'label': '1728.2739.288.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '288.m1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595753
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '144.h1.a1', '144.n1.a1', '144.q1.a1'], 'contains': ['576.b1.a1', '864.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4010, -1, 7165, -1, 3178, -1, 4057, -1], 'generators': [1420, 448], 'label': '1728.2739.288.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '288.n1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595754
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1', '144.i1.a1', '144.o1.a1', '144.r1.a2'], 'contains': ['576.c1.a1', '864.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2167, -1, 4477, -1, 2086, -1, 2874, -1], 'generators': [1420, 1344], 'label': '1728.2739.288.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.o1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595755
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.545', 'aut_weyl_index': 16, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.g1.a1', '24.q1.a1', '24.r1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9473, -1, 9627, -1, 9020, -1, 9151, -1], 'generators': [1, 576, 1600, 768, 2, 4], 'label': '1728.2739.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '8.j1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 89595756
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '36.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a2', '144.i1.a1', '144.o1.a2', '144.r1.a1'], 'contains': ['576.c1.a1', '864.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2167, -1, 4741, -1, 2086, -1, 2946, -1], 'generators': [1420, 640], 'label': '1728.2739.288.o1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '288.o1.a2', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595757
    {'ambient': '1728.2739', 'aut_centralizer_order': 6912, 'aut_label': '432.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1'], 'contains': ['864.a1.a1', '864.b1.a1', '864.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5021, 2276, 4387, 2061, 3960, 8130, 4666, 1796], 'generators': [4, 96], 'label': '1728.2739.432.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.a1.a1', '216.a1.a1'], 'normal_contains': ['864.b1.a1', '864.a1.a1', '864.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.238', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.238', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595758
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.e1.a1', '144.f1.a1', '216.b1.a1', '216.f1.a1', '216.f1.b1'], 'contains': ['864.a1.a1', '864.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1443, -1, 1798, -1, 1873, -1, 2266, -1], 'generators': [1416, 96], 'label': '1728.2739.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595759
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '144.h1.a1', '144.i1.a1', '216.b1.a1', '216.g1.a1'], 'contains': ['864.a1.a1', '864.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1601, -1, 1715, -1, 1697, -1, 2113, -1], 'generators': [1420, 96], 'label': '1728.2739.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595760
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '144.k1.a1', '144.l1.a1', '216.d1.a1', '216.f1.a1', '216.g1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [552, -1, 541, -1, 900, -1, 1098, -1], 'generators': [52], 'label': '1728.2739.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '432.d1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595761
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.b1', '144.k1.b1', '144.l1.b1', '216.d1.a1', '216.f1.b1', '216.g1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [552, -1, 823, -1, 900, -1, 1728, -1], 'generators': [48], 'label': '1728.2739.432.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '432.d1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595762
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1.a1', '144.n1.a1', '144.o1.a1', '144.o1.a2', '216.b1.a1'], 'contains': ['864.b1.a1', '864.d1.a1', '864.e1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3419, -1, 4979, -1, 2652, -1, 3464, -1], 'generators': [100, 1416], 'label': '1728.2739.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595763
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.p1.a1', '144.q1.a1', '144.r1.a1', '144.r1.a2', '216.b1.a1', '216.h1.a1', '216.i1.a1'], 'contains': ['864.c1.a1', '864.d1.a1', '864.e1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3818, -1, 5218, -1, 4115, -1, 4775, -1], 'generators': [4, 1416], 'label': '1728.2739.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '432.f1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595764
    {'ambient': '1728.2739', 'aut_centralizer_order': 1728, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.s1.a1', '144.v1.a1', '144.w1.a1', '144.y1.a1', '216.a1.a1', '216.h1.a1', '216.j1.a1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8365, -1, 8361, -1, 7726, -1, 8025, -1], 'generators': [2], 'label': '1728.2739.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '432.g1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595765
    {'ambient': '1728.2739', 'aut_centralizer_order': 192, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.t1.a1', '144.x1.a1', '144.z1.a1', '216.c1.a1', '216.h1.a1', '216.k1.a1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7641, -1, 7760, -1, 7534, -1, 7889, -1], 'generators': [1422], 'label': '1728.2739.432.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '432.h1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595766
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.h1.a1', '72.ba1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8426, -1, 8604, -1, 8180, -1, 8410, -1], 'generators': [1691, 576, 768, 1134, 4, 1600], 'label': '1728.2739.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '8.k1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 89595767
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1.a1', '144.ba1.a1', '144.bb1.a1', '216.e1.a1', '216.i1.a1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5667, -1, 3805, -1, 4944, -1, 5529, -1], 'generators': [54], 'label': '1728.2739.432.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.g1.a1', 'old_label': '432.i1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595768
    {'ambient': '1728.2739', 'aut_centralizer_order': 3456, 'aut_label': '576.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '288.a1.a1', '288.b1.a1', '288.c1.a1', '288.j1.a1', '288.m1.a1'], 'contains': ['1728.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3229, 4964, 6091, 4495, 2484, 6029, 3387, 3805], 'generators': [576], 'label': '1728.2739.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['64.a1.a1', '288.b1.a1', '288.a1.a1', '288.c1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '1728.2739', 'quotient_action_image': '2.1', 'quotient_action_kernel': '288.426', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595769
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '288.d1.a1', '288.f1.a1', '288.h1.a1', '288.k1.a1', '288.n1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3997, -1, 7165, -1, 3178, -1, 4057, -1], 'generators': [1600], 'label': '1728.2739.576.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '576.b1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595770
    {'ambient': '1728.2739', 'aut_centralizer_order': 576, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '12.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '288.e1.a1', '288.g1.a1', '288.i1.a1', '288.l1.a1', '288.l1.a2', '288.o1.a1', '288.o1.a2'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2167, -1, 4758, -1, 2255, -1, 3095, -1], 'generators': [64], 'label': '1728.2739.576.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '576.c1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595771
    {'ambient': '1728.2739', 'aut_centralizer_order': 6912, 'aut_label': '864.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '288.d1.a1', '288.e1.a1', '432.a1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '432.d1.b1'], 'contains': ['1728.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1566, 4351, 1781, 3938, 1829, 6720, 2189, 3141], 'generators': [96], 'label': '1728.2739.864.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '864.a1.a1', 'normal_contained_in': ['288.a1.a1', '432.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.a1.a1', 'projective_image': '864.665', 'quotient_action_image': '1.1', 'quotient_action_kernel': '864.665', 'quotient_action_kernel_order': 864, 'quotient_fusion': None, 'short_label': '864.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595772
    {'ambient': '1728.2739', 'aut_centralizer_order': 6912, 'aut_label': '864.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.b1.a1', '288.f1.a1', '288.g1.a1', '432.a1.a1', '432.e1.a1'], 'contains': ['1728.a1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4016, 3626, 4888, 2607, 2695, 7410, 3502, 1815], 'generators': [100], 'label': '1728.2739.864.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '864.b1.a1', 'normal_contained_in': ['288.b1.a1', '432.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.b1.a1', 'projective_image': '864.667', 'quotient_action_image': '1.1', 'quotient_action_kernel': '864.667', 'quotient_action_kernel_order': 864, 'quotient_fusion': None, 'short_label': '864.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595773
    {'ambient': '1728.2739', 'aut_centralizer_order': 6912, 'aut_label': '864.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.c1.a1', '288.h1.a1', '288.i1.a1', '432.a1.a1', '432.f1.a1', '432.g1.a1', '432.h1.a1', '432.i1.a1'], 'contains': ['1728.a1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5021, 2880, 5245, 3282, 4425, 8101, 5057, 2478], 'generators': [4], 'label': '1728.2739.864.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '864.c1.a1', 'normal_contained_in': ['288.c1.a1', '432.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.c1.a1', 'projective_image': '864.668', 'quotient_action_image': '1.1', 'quotient_action_kernel': '864.668', 'quotient_action_kernel_order': 864, 'quotient_fusion': None, 'short_label': '864.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595774
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.j1.a1', '288.k1.a1', '288.l1.a1', '288.l1.a2', '432.b1.a1', '432.e1.a1', '432.f1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3263, -1, 5069, -1, 2566, -1, 3315, -1], 'generators': [1416], 'label': '1728.2739.864.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '864.d1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595775
    {'ambient': '1728.2739', 'aut_centralizer_order': 384, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6912, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.m1.a1', '288.n1.a1', '288.o1.a1', '288.o1.a2', '432.c1.a1', '432.e1.a1', '432.f1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3391, -1, 4995, -1, 2402, -1, 3243, -1], 'generators': [1420], 'label': '1728.2739.864.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '864.e1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595776
    {'ambient': '1728.2739', 'aut_centralizer_order': None, 'aut_label': '1728.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': ['576.a1.a1', '576.b1.a1', '576.c1.a1', '864.a1.a1', '864.b1.a1', '864.c1.a1', '864.d1.a1', '864.e1.a1'], 'contains': [], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3358, 3988, 5032, 3610, 2525, 7065, 3351, 2810], 'generators': [], 'label': '1728.2739.1728.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1728.a1.a1', 'normal_contained_in': ['576.a1.a1', '864.b1.a1', '864.a1.a1', '864.c1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1728.a1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 89595777
    {'ambient': '1728.2739', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '384.18267', 'aut_weyl_index': 18, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '27.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8716, -1, 7644, -1, 8463, -1, 8659, -1], 'generators': [1, 96, 4, 48, 576, 2, 8], 'label': '1728.2739.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.14'}
  • id: 89595778
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.d1.a1', '24.m1.a1', '24.n1.a1', '36.a1.a1', '36.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7741, -1, 8674, -1, 7935, -1, 8191, -1], 'generators': [2, 448, 4, 392, 96, 576], 'label': '1728.2739.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595779
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.f1.a1', '24.o1.a1', '24.o1.a2', '36.a1.a1', '36.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6190, -1, 4664, -1, 6733, -1, 6966, -1], 'generators': [2, 640, 4, 200, 96, 576], 'label': '1728.2739.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595780
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '24.h1.a1', '24.k1.a1', '24.k1.b1', '24.l1.a1', '24.l1.b1', '36.b1.a1', '36.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2389, -1, 1676, -1, 2891, -1, 2216, -1], 'generators': [4, 576, 640, 200, 816, 96], 'label': '1728.2739.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595781
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.46139', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '6.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8844, 2457, 8545, 3701, 8756, 6096, 8923, 4007], 'generators': [1, 4, 1600, 1416, 96, 576, 1344, 2], 'label': '1728.2739.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.87'}
  • id: 89595782
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.i1.a1', '24.j1.a1', '24.p1.a1', '24.p1.a2', '36.c1.a1', '36.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5473, -1, 4282, -1, 4836, -1, 5289, -1], 'generators': [822, 576, 640, 200, 96, 4], 'label': '1728.2739.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595783
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.q1.a1', '36.i1.a1', '36.l1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9109, -1, 9374, -1, 9409, -1, 9304, -1], 'generators': [1, 576, 4, 96, 832, 2], 'label': '1728.2739.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595784
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4033', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '24.r1.a1', '36.i1.a1', '36.m1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9316, -1, 9555, -1, 9207, -1, 9482, -1], 'generators': [1, 576, 1600, 96, 2, 4], 'label': '1728.2739.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 89595785
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1'], 'contains': ['24.e1.a1', '24.g1.a1', '24.i1.a1', '36.h1.a1', '36.n1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6667, -1, 2650, -1, 5719, -1, 6154, -1], 'generators': [2, 576, 96, 48, 64, 4], 'label': '1728.2739.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.g1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595786
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4033', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1'], 'contains': ['24.e1.a1', '24.h1.a1', '24.j1.a1', '36.h1.a1', '36.o1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5923, -1, 2808, -1, 5896, -1, 6309, -1], 'generators': [2, 576, 768, 48, 4, 96], 'label': '1728.2739.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595787
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.j1.a1', '36.j1.a1', '36.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5263, -1, 3521, -1, 5366, -1, 5844, -1], 'generators': [74, 576, 64, 48, 4, 96], 'label': '1728.2739.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595788
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1'], 'contains': ['24.f1.a1', '24.h1.a1', '24.i1.a1', '36.j1.a1', '36.q1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5705, -1, 3382, -1, 5210, -1, 5708, -1], 'generators': [1422, 576, 1344, 48, 4, 96], 'label': '1728.2739.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595789
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.a1', '48.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3743, 3736, 5035, 3382, 3580, 6163, 4049, 3685], 'generators': [4, 576, 96, 64, 768], 'label': '1728.2739.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.b1.a1', '32.a1.a1', '32.c1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595790
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.c1.a1', '48.d1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1918, 7795, 2207, 7111, 1740, 2297, 2142, 7471], 'generators': [1416, 576, 96, 640, 1344], 'label': '1728.2739.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595791
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '16.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '48.e1.a1', '48.f1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1698, 5912, 3793, 5378, 1521, 4091, 1955, 5703], 'generators': [1420, 576, 96, 640, 1344], 'label': '1728.2739.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595792
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8418', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.g1.a1', '18.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8503, 3858, 7840, 2434, 8226, 7429, 8451, 2727], 'generators': [1691, 4, 64, 1416, 96, 576, 768, 1134], 'label': '1728.2739.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
  • id: 89595793
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 32, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.e1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '48.g1.a1', '48.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1209, -1, 928, -1, 1051, -1, 1104, -1], 'generators': [52, 576, 64, 96, 768], 'label': '1728.2739.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595794
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 32, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.e1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '48.g1.b1', '48.h1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1209, -1, 1319, -1, 1051, -1, 1414, -1], 'generators': [48, 576, 64, 96, 768], 'label': '1728.2739.16.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.d1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595795
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.e1.a1', '48.i1.a1', '48.j1.a1', '48.j1.a2'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3265, -1, 5661, -1, 1957, -1, 3132, -1], 'generators': [100, 576, 1416, 640, 1344], 'label': '1728.2739.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595796
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.i1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.e1.a1', '48.k1.a1', '48.l1.a1', '48.l1.a2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3490, -1, 6474, -1, 3808, -1, 4249, -1], 'generators': [4, 576, 1416, 640, 1344], 'label': '1728.2739.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595797
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.h1.a1', '8.j1.a1'], 'contains': ['32.c1.a1', '48.m1.a1', '48.n1.a1', '48.p1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8081, -1, 8310, -1, 7732, -1, 8014, -1], 'generators': [2, 576, 64, 768, 4], 'label': '1728.2739.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.g1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595798
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.h1.a1', '8.k1.a1'], 'contains': ['32.c1.a1', '48.o1.a1', '48.q1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6500, -1, 8074, -1, 7164, -1, 7516, -1], 'generators': [1422, 576, 4, 640, 1344], 'label': '1728.2739.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.h1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 89595799
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 32, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.i1.a1'], 'contains': ['32.c1.a1', '48.r1.a1', '48.s1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4802, -1, 5333, -1, 4237, -1, 4624, -1], 'generators': [54, 576, 64, 4, 768], 'label': '1728.2739.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.i1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 89595800
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 72, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.h1.a1', '36.j1.a1', '54.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7106, -1, 3610, -1, 6072, -1, 6463, -1], 'generators': [2, 576, 96, 1416, 816, 4], 'label': '1728.2739.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 89595801
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.207', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.i1.a1', '54.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8968, -1, 8027, -1, 8838, -1, 8992, -1], 'generators': [1, 576, 4, 1416, 2, 96], 'label': '1728.2739.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.6'}
  • id: 89595802
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 216, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.k1.a1', '54.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8666, -1, 7802, -1, 8427, -1, 8631, -1], 'generators': [1691, 4, 96, 1032, 576, 1134], 'label': '1728.2739.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
  • id: 89595803
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.186', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.h1.a1', '12.a1.a1', '12.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6809, 2750, 7917, 2744, 7355, 7103, 7442, 3040], 'generators': [2, 1344, 640, 1416, 576, 96, 4], 'label': '1728.2739.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595804
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['36.d1.a1', '36.l1.a1', '36.m1.a1', '54.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9741, -1, 9335, -1, 9558, -1, 9621, -1], 'generators': [1, 448, 4, 392, 2, 96], 'label': '1728.2739.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '18.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595805
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['36.e1.a1', '36.f1.a1', '36.g1.a1', '36.n1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1', '54.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5927, -1, 2961, -1, 5529, -1, 5987, -1], 'generators': [2, 640, 96, 200, 816, 4], 'label': '1728.2739.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '18.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595806
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.e1.a1', '48.i1.a1', '48.k1.a1', '72.b1.a1', '72.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4145, -1, 7338, -1, 4035, -1, 4447, -1], 'generators': [4, 448, 392, 96, 576], 'label': '1728.2739.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595807
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.f1.a1', '48.j1.a1', '48.j1.a2', '48.l1.a1', '48.l1.a2', '72.b1.a1', '72.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2389, -1, 4343, -1, 3339, -1, 3837, -1], 'generators': [4, 640, 200, 96, 576], 'label': '1728.2739.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595808
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['48.a1.a1', '48.m1.a1', '48.n1.a1', '72.a1.a1', '72.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8314, -1, 8930, -1, 8305, -1, 8515, -1], 'generators': [2, 4, 96, 1600, 576], 'label': '1728.2739.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595809
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '48.o1.a1', '72.e1.a1', '72.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7492, -1, 7995, -1, 7527, -1, 7834, -1], 'generators': [398, 448, 96, 576, 4], 'label': '1728.2739.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595810
    {'ambient': '1728.2739', 'aut_centralizer_order': 144, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.b1.a1', '48.p1.a1', '72.a1.a1', '72.j1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6801, -1, 3373, -1, 6828, -1, 7059, -1], 'generators': [2, 4, 96, 64, 576], 'label': '1728.2739.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595811
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['48.b1.a1', '48.q1.a1', '72.e1.a1', '72.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5661, -1, 4651, -1, 6640, -1, 6684, -1], 'generators': [206, 640, 96, 576, 4], 'label': '1728.2739.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595812
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.c1.a1', '12.g1.a1', '12.i1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '48.g1.b1', '72.f1.a1', '72.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2828, -1, 2038, -1, 3124, -1, 2318, -1], 'generators': [4, 576, 48, 64, 96], 'label': '1728.2739.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595851
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.51', 'aut_weyl_index': 216, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.e1.a1'], 'contains': ['72.j1.a1', '72.l1.a1', '72.n1.a1', '108.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6318, -1, 2516, -1, 5703, -1, 6166, -1], 'generators': [2, 96, 48, 64, 4], 'label': '1728.2739.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.n1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 89595813
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.545', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.c1.a1', '12.h1.a1', '12.j1.a1'], 'contains': ['48.b1.a1', '48.h1.a1', '48.h1.b1', '72.f1.a1', '72.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2621, -1, 2220, -1, 2921, -1, 2496, -1], 'generators': [4, 576, 48, 96, 768], 'label': '1728.2739.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.h1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595814
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.30413', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.g1.a1', '12.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2489, 8741, 1585, 8168, 3022, 1396, 2216, 8521], 'generators': [4, 1344, 640, 1416, 576, 48, 96], 'label': '1728.2739.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.238'}
  • id: 89595815
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.d1.a1', '12.g1.a1', '12.j1.a1'], 'contains': ['48.b1.a1', '48.r1.a1', '72.g1.a1', '72.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5423, -1, 3774, -1, 4604, -1, 5111, -1], 'generators': [54, 576, 96, 64, 4], 'label': '1728.2739.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595816
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.545', 'aut_weyl_index': 16, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.d1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.b1.a1', '48.s1.a1', '72.g1.a1', '72.o1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4935, -1, 4020, -1, 4806, -1, 5289, -1], 'generators': [54, 576, 96, 4, 768], 'label': '1728.2739.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595817
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.c1.a1'], 'contains': ['48.d1.a1', '48.g1.a1', '48.h1.a1', '72.p1.a1', '72.q1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [346, -1, 366, -1, 1228, -1, 950, -1], 'generators': [820, 576, 200, 96, 640], 'label': '1728.2739.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595818
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.c1.a1'], 'contains': ['48.d1.a1', '48.g1.b1', '48.h1.b1', '72.p1.b1', '72.q1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [346, -1, 1272, -1, 1228, -1, 1569, -1], 'generators': [200, 576, 816, 96, 640], 'label': '1728.2739.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.k1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595819
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.c1.a1'], 'contains': ['48.f1.a1', '48.g1.a1', '48.h1.b1', '72.r1.a1', '72.s1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [673, -1, 637, -1, 712, -1, 1259, -1], 'generators': [1420, 576, 48, 96, 1344], 'label': '1728.2739.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.l1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595820
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 48, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.c1.a1'], 'contains': ['48.f1.a1', '48.g1.b1', '48.h1.a1', '72.r1.a1', '72.s1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [673, -1, 1025, -1, 712, -1, 784, -1], 'generators': [76, 576, 48, 96, 64], 'label': '1728.2739.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.l1.b1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 89595821
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.a1'], 'contains': ['48.k1.a1', '48.m1.a1', '48.o1.a1', '72.t1.a1', '72.v1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7961, -1, 8362, -1, 7935, -1, 8353, -1], 'generators': [2, 448, 1416, 576, 4], 'label': '1728.2739.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595822
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.a1'], 'contains': ['48.k1.a1', '48.n1.a1', '48.o1.a1', '72.t1.a1', '72.w1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7727, -1, 8647, -1, 8120, -1, 8191, -1], 'generators': [2, 1408, 1416, 576, 4], 'label': '1728.2739.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595823
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.b1.a1'], 'contains': ['48.l1.a1', '48.p1.a1', '48.q1.a1', '72.t1.a1', '72.x1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6477, -1, 6113, -1, 7013, -1, 7222, -1], 'generators': [2, 640, 1416, 576, 4], 'label': '1728.2739.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.o1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595824
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1152, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.b1.a1'], 'contains': ['48.l1.a2', '48.p1.a1', '48.q1.a1', '72.t1.a1', '72.x1.a2'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6477, -1, 6588, -1, 7013, -1, 7383, -1], 'generators': [2, 1344, 1416, 576, 4], 'label': '1728.2739.24.o1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.o1.a2', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595825
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.30413', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.i1.a1', '12.d1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5106, 5629, 4282, 5351, 4574, 4360, 5059, 5675], 'generators': [54, 1344, 640, 1416, 576, 96, 4], 'label': '1728.2739.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.238'}
  • id: 89595826
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.d1.a1'], 'contains': ['48.l1.a1', '48.r1.a1', '48.s1.a1', '72.u1.a1', '72.y1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5186, -1, 5155, -1, 4413, -1, 4779, -1], 'generators': [822, 576, 1416, 4, 640], 'label': '1728.2739.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '24.p1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595827
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 96, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.d1.a1'], 'contains': ['48.l1.a2', '48.r1.a1', '48.s1.a1', '72.u1.a1', '72.y1.a2'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5186, -1, 4859, -1, 4413, -1, 4944, -1], 'generators': [54, 576, 1416, 4, 1344], 'label': '1728.2739.24.p1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '24.p1.a2', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595828
    {'ambient': '1728.2739', 'aut_centralizer_order': 12, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.e1.a1'], 'contains': ['48.n1.a1', '72.z1.a1', '72.bb1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9386, -1, 9699, -1, 9539, -1, 9484, -1], 'generators': [1, 576, 256, 2, 4], 'label': '1728.2739.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '24.q1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 89595829
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.545', 'aut_weyl_index': 16, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.f1.a1'], 'contains': ['48.m1.a1', '72.z1.a1', '72.bc1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9594, -1, 9869, -1, 9380, -1, 9623, -1], 'generators': [1, 576, 2, 4, 1600], 'label': '1728.2739.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '24.r1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 89595830
    {'ambient': '1728.2739', 'aut_centralizer_order': 2, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 54, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8806, -1, 7711, -1, 8636, -1, 8814, -1], 'generators': [1, 48], 'label': '1728.2739.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
  • id: 89595831
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.d1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1785, 7331, 1830, 6637, 1415, 2844, 1955, 6873], 'generators': [96, 64, 768, 576], 'label': '1728.2739.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normal_contains': ['64.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595832
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '32.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.e1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '96.d1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3529, 5387, 5661, 3117, 2045, 4695, 3295, 3317], 'generators': [100, 64, 768, 576], 'label': '1728.2739.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '864.667', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595833
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '32.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '96.e1.a1', '96.f1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3844, 3444, 7016, 4877, 4077, 6547, 4558, 5095], 'generators': [4, 64, 768, 576], 'label': '1728.2739.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '288.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '864.668', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
  • id: 89595834
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.e1.a1', '16.f1.a1'], 'contains': ['64.a1.a1', '96.g1.a1', '96.h1.a1', '96.h1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2787, -1, 6243, -1, 1870, -1, 3008, -1], 'generators': [1416, 640, 1344, 576], 'label': '1728.2739.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595835
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.e1.a1', '16.f1.a1'], 'contains': ['64.a1.a1', '96.i1.a1', '96.j1.a1', '96.j1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2917, -1, 6357, -1, 1743, -1, 2760, -1], 'generators': [1420, 640, 1344, 576], 'label': '1728.2739.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '1728.2739', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 89595836
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4033', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.f1.a1', '12.g1.a1', '12.h1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5962, -1, 3038, -1, 5716, -1, 6151, -1], 'generators': [2, 768, 96, 48, 576, 64, 4], 'label': '1728.2739.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.102'}
  • id: 89595837
    {'ambient': '1728.2739', 'aut_centralizer_order': 96, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.e1.a1', '72.t1.a1', '108.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7770, -1, 7402, -1, 7327, -1, 7658, -1], 'generators': [2, 4, 1416, 96, 576], 'label': '1728.2739.36.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 89595838
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 72, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.f1.a1', '72.p1.a1', '72.p1.b1', '72.r1.a1', '108.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1821, -1, 2335, -1, 2707, -1, 2683, -1], 'generators': [4, 576, 1416, 816, 96], 'label': '1728.2739.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 89595839
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.209', 'aut_weyl_index': 72, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.g1.a1', '72.u1.a1', '108.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6525, -1, 4414, -1, 5260, -1, 5686, -1], 'generators': [822, 576, 1416, 96, 4], 'label': '1728.2739.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 89595840
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.d1.a1'], 'contains': ['72.c1.a1', '72.h1.a1', '72.i1.a1', '72.v1.a1', '72.w1.a1', '108.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9004, -1, 8927, -1, 8518, -1, 8702, -1], 'generators': [2, 448, 392, 96, 4], 'label': '1728.2739.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595841
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.e1.a1'], 'contains': ['72.d1.a1', '72.j1.a1', '72.k1.a1', '72.x1.a1', '72.x1.a2', '108.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6097, -1, 4095, -1, 6424, -1, 6873, -1], 'generators': [2, 640, 200, 96, 4], 'label': '1728.2739.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595842
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.e1.a1'], 'contains': ['72.d1.a1', '72.l1.a1', '72.m1.a1', '72.q1.a1', '72.q1.b1', '72.s1.a1', '72.s1.b1', '108.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1588, -1, 1778, -1, 2480, -1, 1756, -1], 'generators': [4, 640, 200, 816, 96], 'label': '1728.2739.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.f1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595843
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.e1.a1'], 'contains': ['72.d1.a1', '72.n1.a1', '72.o1.a1', '72.y1.a1', '72.y1.a2', '108.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4965, -1, 3151, -1, 5033, -1, 5487, -1], 'generators': [822, 640, 200, 96, 4], 'label': '1728.2739.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.g1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595844
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '18.a1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.g1.a1', '108.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6999, -1, 2959, -1, 6061, -1, 6387, -1], 'generators': [2, 576, 48, 4, 96], 'label': '1728.2739.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '36.h1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595845
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '72.z1.a1', '108.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9268, -1, 9557, -1, 9221, -1, 9317, -1], 'generators': [1, 576, 96, 2, 4], 'label': '1728.2739.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595846
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.j1.a1', '18.a1.a1'], 'contains': ['72.e1.a1', '72.f1.a1', '72.g1.a1', '108.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7106, -1, 3538, -1, 5851, -1, 5917, -1], 'generators': [74, 576, 48, 4, 96], 'label': '1728.2739.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595847
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '864.4033', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '12.e1.a1', '12.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9109, -1, 9385, -1, 8984, -1, 9108, -1], 'generators': [1, 1600, 4, 96, 576, 768, 2], 'label': '1728.2739.4.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.e1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 89595848
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 864, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '18.c1.a1'], 'contains': ['72.e1.a1', '72.ba1.a1', '108.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8608, -1, 8426, -1, 8775, -1, 8927, -1], 'generators': [1691, 4, 96, 576, 1134], 'label': '1728.2739.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.k1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595849
    {'ambient': '1728.2739', 'aut_centralizer_order': 24, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.14', 'aut_weyl_index': 432, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.d1.a1'], 'contains': ['72.h1.a1', '72.bb1.a1', '108.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9682, -1, 9389, -1, 9918, -1, 9761, -1], 'generators': [1, 4, 96, 1408, 2], 'label': '1728.2739.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.l1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 89595850
    {'ambient': '1728.2739', 'aut_centralizer_order': 8, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.d1.a1'], 'contains': ['72.h1.a1', '72.bc1.a1', '108.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9918, -1, 9727, -1, 9729, -1, 9926, -1], 'generators': [1, 1600, 96, 2, 4], 'label': '1728.2739.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.m1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595852
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.e1.a1'], 'contains': ['72.j1.a1', '72.m1.a1', '72.o1.a1', '108.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5744, -1, 2648, -1, 5956, -1, 6296, -1], 'generators': [2, 768, 48, 4, 96], 'label': '1728.2739.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.o1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595853
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.e1.a1'], 'contains': ['72.k1.a1', '72.l1.a1', '72.o1.a1', '108.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5424, -1, 2851, -1, 5540, -1, 6023, -1], 'generators': [74, 64, 48, 4, 96], 'label': '1728.2739.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.p1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595854
    {'ambient': '1728.2739', 'aut_centralizer_order': 4, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.230', 'aut_weyl_index': 72, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.e1.a1'], 'contains': ['72.k1.a1', '72.m1.a1', '72.n1.a1', '108.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5549, -1, 2743, -1, 5419, -1, 5826, -1], 'generators': [1422, 1344, 48, 4, 96], 'label': '1728.2739.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.q1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 89595855
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.e1.a1', '144.a1.a1', '144.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4881, -1, 7659, -1, 4234, -1, 4696, -1], 'generators': [4, 96, 1600, 576], 'label': '1728.2739.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595856
    {'ambient': '1728.2739', 'aut_centralizer_order': 288, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 576, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.f1.a1', '144.a1.a1', '144.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3345, -1, 3720, -1, 3766, -1, 3994, -1], 'generators': [4, 96, 64, 576], 'label': '1728.2739.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '432.238', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 89595857
    {'ambient': '1728.2739', 'aut_centralizer_order': 48, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1'], 'contains': ['96.a1.a1', '96.g1.a1', '144.d1.a1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2243, -1, 5163, -1, 2385, -1, 3594, -1], 'generators': [392, 96, 576, 448], 'label': '1728.2739.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '864.665', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}